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Номер 7, страница 47, часть 1 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.
Тип: рабочая тетрадь
Издательство: Просвещение
Год издания: 2021 - 2026
Часть: 1
Цвет обложки: синий
ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)
Популярные ГДЗ в 9 классе
Часть 1. Глава 1. Кинематика. Параграф 10. Равномерное движение по окружности. Угловая скорость. Период и частота вращения - номер 7, страница 47.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434947 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "47" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/10-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434806 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Book {#1049 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:4 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1060 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #original: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Term {#1072 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1074 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Term {#1080 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_country" => Illuminate\Database\Eloquent\Collection {#1064} "field_city" => Illuminate\Database\Eloquent\Collection {#1066} "field_series" => Illuminate\Database\Eloquent\Collection {#1068} "field_umk" => Illuminate\Database\Eloquent\Collection {#1069} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434806 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1083} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1188 #items: array:3 [ 0 => App\Models\Branch {#1198 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434806 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1199 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1201 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434806 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1199} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1200} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1201} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1202 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:1 [ 0 => App\Models\Term {#1203 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1205 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1206} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1205} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1204} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1207 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434818 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Равномерное движение по окружности. Угловая скорость. Период и частота вращения" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211 #items: array:1 [ 0 => App\Models\Term {#1208 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "44" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1210 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1287 #items: array:1 [ 0 => App\Models\Branch {#1209 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Term {#1212 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1214 #items: array:1 [ 0 => App\Models\Book {#1215 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] …6 } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:1 [ 0 => App\Models\Branch {#1248 …30} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1213} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1214} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1247} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434818 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Равномерное движение по окружности. Угловая скорость. Период и частота вращения" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211} "field_page_start" => "44" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1210} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1287} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:2 [ 0 => App\Models\Element {#1182 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1698335 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1173 #items: array:1 [ 0 => App\Models\Edition {#1181 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1178 #items: array:1 [ 0 => App\Models\Term {#1180 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1179 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1176 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1177 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1178} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1179} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1176} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1177} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1434947" "type" => "task" ] "text" => "<p><strong>7.</strong> Изобразите на окружностях (рис. 37) положения точечных тел, законы движения которых приведены в задании 6, в моменты времени $\text{t}$, равные 0, 1, 2 и 3 с. Угол $\phi$ отсчитывайте от оси $\text{X}$ против хода часовой стрелки, если он положителен, и по ходу часовой стрелки, если он отрицателен.</p><p>Рис. 37</p>" "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "1977" "height" => 1570 "path" => "/media/fizika_09/grachev-rt/0-10/7-1.webp?ts=1759402648" ] ] ] #original: array:7 [ "id" => 1698335 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1173} "task" => array:2 [ "refs" => "1434947" "type" => "task" ] "text" => "<p><strong>7.</strong> Изобразите на окружностях (рис. 37) положения точечных тел, законы движения которых приведены в задании 6, в моменты времени $\text{t}$, равные 0, 1, 2 и 3 с. Угол $\phi$ отсчитывайте от оси $\text{X}$ против хода часовой стрелки, если он положителен, и по ходу часовой стрелки, если он отрицателен.</p><p>Рис. 37</p>" "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "1977" "height" => 1570 "path" => "/media/fizika_09/grachev-rt/0-10/7-1.webp?ts=1759402648" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1175 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1734321 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161 #items: array:1 [ 0 => App\Models\Edition {#1174 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1172 #items: array:1 [ 0 => App\Models\Term {#1171 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1169 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1170 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1167 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1172} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1169} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1170} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1167} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1434947" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p> <p>Законы движения точечных тел (из задания 6):</p> <p>а) $\phi(t) = \frac{\pi}{2} t$</p> <p>б) $\phi(t) = \pi(1-t)$</p> <p>в) $\phi(t) = -\frac{\pi}{4} t$</p> <p>г) $\phi(t) = \frac{\pi}{4} + \frac{\pi}{2} t$</p> <p>д) $\phi(t) = \frac{\pi}{2} - \frac{\pi}{4} t$</p> <p>Моменты времени: $t_0 = 0$ с, $t_1 = 1$ с, $t_2 = 2$ с, $t_3 = 3$ с.</p> <p><strong>Найти:</strong></p> <p>Положения точечных тел $\phi$ в заданные моменты времени.</p> <p><strong>Решение:</strong></p> <p>Для каждого закона движения рассчитаем угловое положение $\phi$ в моменты времени $t = 0, 1, 2, 3$ с. Согласно условию, положительные углы отсчитываются от оси Х против часовой стрелки, а отрицательные — по часовой стрелке.</p> <p><strong>а)</strong></p> <p>Закон движения: $\phi(t) = \frac{\pi}{2} t$.</p> <p>При $t = 0$ с: $\phi = \frac{\pi}{2} \cdot 0 = 0$ рад. Положение на положительной части оси Х.</p> <p>При $t = 1$ с: $\phi = \frac{\pi}{2} \cdot 1 = \frac{\pi}{2}$ рад ($90^\circ$). Положение на положительной части оси Y.</p> <p>При $t = 2$ с: $\phi = \frac{\pi}{2} \cdot 2 = \pi$ рад ($180^\circ$). Положение на отрицательной части оси Х.</p> <p>При $t = 3$ с: $\phi = \frac{\pi}{2} \cdot 3 = \frac{3\pi}{2}$ рад ($270^\circ$). Положение на отрицательной части оси Y.</p> <p><strong>Ответ:</strong> В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $0$, $\frac{\pi}{2}$, $\pi$ и $\frac{3\pi}{2}$ радиан, отсчитанным против часовой стрелки от положительного направления оси Х.</p> <p><strong>б)</strong></p> <p>Закон движения: $\phi(t) = \pi(1-t) = \pi - \pi t$.</p> <p>При $t = 0$ с: $\phi = \pi(1-0) = \pi$ рад ($180^\circ$). Положение на отрицательной части оси Х.</p> <p>При $t = 1$ с: $\phi = \pi(1-1) = 0$ рад. Положение на положительной части оси Х.</p> <p>При $t = 2$ с: $\phi = \pi(1-2) = -\pi$ рад ($-180^\circ$). Угол отрицательный, отсчитывается по часовой стрелке. Положение совпадает с углом $\pi$, т.е. на отрицательной части оси Х.</p> <p>При $t = 3$ с: $\phi = \pi(1-3) = -2\pi$ рад ($-360^\circ$). Угол отрицательный, отсчитывается по часовой стрелке. Положение совпадает с углом $0$, т.е. на положительной части оси Х.</p> <p><strong>Ответ:</strong> В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $\pi$, $0$, $-\pi$ (эквивалентно $\pi$), $-2\pi$ (эквивалентно $0$) радиан. Тело оказывается поочередно на отрицательной и положительной частях оси Х.</p> <p><strong>в)</strong></p> <p>Закон движения: $\phi(t) = -\frac{\pi}{4} t$.</p> <p>При $t = 0$ с: $\phi = -\frac{\pi}{4} \cdot 0 = 0$ рад. Положение на положительной части оси Х.</p> <p>При $t = 1$ с: $\phi = -\frac{\pi}{4}$ рад ($-45^\circ$). Угол отсчитывается по часовой стрелке, положение на биссектрисе IV координатного угла.</p> <p>При $t = 2$ с: $\phi = -\frac{\pi}{4} \cdot 2 = -\frac{\pi}{2}$ рад ($-90^\circ$). Угол отсчитывается по часовой стрелке. Положение на отрицательной части оси Y.</p> <p>При $t = 3$ с: $\phi = -\frac{\pi}{4} \cdot 3 = -\frac{3\pi}{4}$ рад ($-135^\circ$). Угол отсчитывается по часовой стрелке, положение на биссектрисе III координатного угла.</p> <p><strong>Ответ:</strong> В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $0$, $-\frac{\pi}{4}$, $-\frac{\pi}{2}$ и $-\frac{3\pi}{4}$ радиан, отсчитанным по часовой стрелке (кроме $t=0$).</p> <p><strong>г)</strong></p> <p>Закон движения: $\phi(t) = \frac{\pi}{4} + \frac{\pi}{2} t$.</p> <p>При $t = 0$ с: $\phi = \frac{\pi}{4} + \frac{\pi}{2} \cdot 0 = \frac{\pi}{4}$ рад ($45^\circ$). Положение на биссектрисе I координатного угла.</p> <p>При $t = 1$ с: $\phi = \frac{\pi}{4} + \frac{\pi}{2} = \frac{3\pi}{4}$ рад ($135^\circ$). Положение на биссектрисе II координатного угла.</p> <p>При $t = 2$ с: $\phi = \frac{\pi}{4} + \pi = \frac{5\pi}{4}$ рад ($225^\circ$). Положение на биссектрисе III координатного угла.</p> <p>При $t = 3$ с: $\phi = \frac{\pi}{4} + \frac{3\pi}{2} = \frac{7\pi}{4}$ рад ($315^\circ$). Положение на биссектрисе IV координатного угла.</p> <p><strong>Ответ:</strong> В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $\frac{\pi}{4}$, $\frac{3\pi}{4}$, $\frac{5\pi}{4}$ и $\frac{7\pi}{4}$ радиан, отсчитанным против часовой стрелки.</p> <p><strong>д)</strong></p> <p>Закон движения: $\phi(t) = \frac{\pi}{2} - \frac{\pi}{4} t$.</p> <p>При $t = 0$ с: $\phi = \frac{\pi}{2} - 0 = \frac{\pi}{2}$ рад ($90^\circ$). Положение на положительной части оси Y.</p> <p>При $t = 1$ с: $\phi = \frac{\pi}{2} - \frac{\pi}{4} = \frac{\pi}{4}$ рад ($45^\circ$). Положение на биссектрисе I координатного угла.</p> <p>При $t = 2$ с: $\phi = \frac{\pi}{2} - \frac{\pi}{2} = 0$ рад. Положение на положительной части оси Х.</p> <p>При $t = 3$ с: $\phi = \frac{\pi}{2} - \frac{3\pi}{4} = -\frac{\pi}{4}$ рад ($-45^\circ$). Угол отсчитывается по часовой стрелке, положение на биссектрисе IV координатного угла.</p> <p><strong>Ответ:</strong> В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $\frac{\pi}{2}$, $\frac{\pi}{4}$, $0$ и $-\frac{\pi}{4}$ радиан.</p>" ] #original: array:6 [ "id" => 1734321 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161} "task" => array:2 [ "refs" => "1434947" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p> <p>Законы движения точечных тел (из задания 6):</p> <p>а) $\phi(t) = \frac{\pi}{2} t$</p> <p>б) $\phi(t) = \pi(1-t)$</p> <p>в) $\phi(t) = -\frac{\pi}{4} t$</p> <p>г) $\phi(t) = \frac{\pi}{4} + \frac{\pi}{2} t$</p> <p>д) $\phi(t) = \frac{\pi}{2} - \frac{\pi}{4} t$</p> <p>Моменты времени: $t_0 = 0$ с, $t_1 = 1$ с, $t_2 = 2$ с, $t_3 = 3$ с.</p> <p><strong>Найти:</strong></p> <p>Положения точечных тел $\phi$ в заданные моменты времени.</p> <p><strong>Решение:</strong></p> <p>Для каждого закона движения рассчитаем угловое положение $\phi$ в моменты времени $t = 0, 1, 2, 3$ с. Согласно условию, положительные углы отсчитываются от оси Х против часовой стрелки, а отрицательные — по часовой стрелке.</p> <p><strong>а)</strong></p> <p>Закон движения: $\phi(t) = \frac{\pi}{2} t$.</p> <p>При $t = 0$ с: $\phi = \frac{\pi}{2} \cdot 0 = 0$ рад. Положение на положительной части оси Х.</p> <p>При $t = 1$ с: $\phi = \frac{\pi}{2} \cdot 1 = \frac{\pi}{2}$ рад ($90^\circ$). Положение на положительной части оси Y.</p> <p>При $t = 2$ с: $\phi = \frac{\pi}{2} \cdot 2 = \pi$ рад ($180^\circ$). Положение на отрицательной части оси Х.</p> <p>При $t = 3$ с: $\phi = \frac{\pi}{2} \cdot 3 = \frac{3\pi}{2}$ рад ($270^\circ$). Положение на отрицательной части оси Y.</p> <p><strong>Ответ:</strong> В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $0$, $\frac{\pi}{2}$, $\pi$ и $\frac{3\pi}{2}$ радиан, отсчитанным против часовой стрелки от положительного направления оси Х.</p> <p><strong>б)</strong></p> <p>Закон движения: $\phi(t) = \pi(1-t) = \pi - \pi t$.</p> <p>При $t = 0$ с: $\phi = \pi(1-0) = \pi$ рад ($180^\circ$). Положение на отрицательной части оси Х.</p> <p>При $t = 1$ с: $\phi = \pi(1-1) = 0$ рад. Положение на положительной части оси Х.</p> <p>При $t = 2$ с: $\phi = \pi(1-2) = -\pi$ рад ($-180^\circ$). Угол отрицательный, отсчитывается по часовой стрелке. Положение совпадает с углом $\pi$, т.е. на отрицательной части оси Х.</p> <p>При $t = 3$ с: $\phi = \pi(1-3) = -2\pi$ рад ($-360^\circ$). Угол отрицательный, отсчитывается по часовой стрелке. Положение совпадает с углом $0$, т.е. на положительной части оси Х.</p> <p><strong>Ответ:</strong> В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $\pi$, $0$, $-\pi$ (эквивалентно $\pi$), $-2\pi$ (эквивалентно $0$) радиан. Тело оказывается поочередно на отрицательной и положительной частях оси Х.</p> <p><strong>в)</strong></p> <p>Закон движения: $\phi(t) = -\frac{\pi}{4} t$.</p> <p>При $t = 0$ с: $\phi = -\frac{\pi}{4} \cdot 0 = 0$ рад. Положение на положительной части оси Х.</p> <p>При $t = 1$ с: $\phi = -\frac{\pi}{4}$ рад ($-45^\circ$). Угол отсчитывается по часовой стрелке, положение на биссектрисе IV координатного угла.</p> <p>При $t = 2$ с: $\phi = -\frac{\pi}{4} \cdot 2 = -\frac{\pi}{2}$ рад ($-90^\circ$). Угол отсчитывается по часовой стрелке. Положение на отрицательной части оси Y.</p> <p>При $t = 3$ с: $\phi = -\frac{\pi}{4} \cdot 3 = -\frac{3\pi}{4}$ рад ($-135^\circ$). Угол отсчитывается по часовой стрелке, положение на биссектрисе III координатного угла.</p> <p><strong>Ответ:</strong> В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $0$, $-\frac{\pi}{4}$, $-\frac{\pi}{2}$ и $-\frac{3\pi}{4}$ радиан, отсчитанным по часовой стрелке (кроме $t=0$).</p> <p><strong>г)</strong></p> <p>Закон движения: $\phi(t) = \frac{\pi}{4} + \frac{\pi}{2} t$.</p> <p>При $t = 0$ с: $\phi = \frac{\pi}{4} + \frac{\pi}{2} \cdot 0 = \frac{\pi}{4}$ рад ($45^\circ$). Положение на биссектрисе I координатного угла.</p> <p>При $t = 1$ с: $\phi = \frac{\pi}{4} + \frac{\pi}{2} = \frac{3\pi}{4}$ рад ($135^\circ$). Положение на биссектрисе II координатного угла.</p> <p>При $t = 2$ с: $\phi = \frac{\pi}{4} + \pi = \frac{5\pi}{4}$ рад ($225^\circ$). Положение на биссектрисе III координатного угла.</p> <p>При $t = 3$ с: $\phi = \frac{\pi}{4} + \frac{3\pi}{2} = \frac{7\pi}{4}$ рад ($315^\circ$). Положение на биссектрисе IV координатного угла.</p> <p><strong>Ответ:</strong> В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $\frac{\pi}{4}$, $\frac{3\pi}{4}$, $\frac{5\pi}{4}$ и $\frac{7\pi}{4}$ радиан, отсчитанным против часовой стрелки.</p> <p><strong>д)</strong></p> <p>Закон движения: $\phi(t) = \frac{\pi}{2} - \frac{\pi}{4} t$.</p> <p>При $t = 0$ с: $\phi = \frac{\pi}{2} - 0 = \frac{\pi}{2}$ рад ($90^\circ$). Положение на положительной части оси Y.</p> <p>При $t = 1$ с: $\phi = \frac{\pi}{2} - \frac{\pi}{4} = \frac{\pi}{4}$ рад ($45^\circ$). Положение на биссектрисе I координатного угла.</p> <p>При $t = 2$ с: $\phi = \frac{\pi}{2} - \frac{\pi}{2} = 0$ рад. Положение на положительной части оси Х.</p> <p>При $t = 3$ с: $\phi = \frac{\pi}{2} - \frac{3\pi}{4} = -\frac{\pi}{4}$ рад ($-45^\circ$). Угол отсчитывается по часовой стрелке, положение на биссектрисе IV координатного угла.</p> <p><strong>Ответ:</strong> В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $\frac{\pi}{2}$, $\frac{\pi}{4}$, $0$ и $-\frac{\pi}{4}$ радиан.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1434948" "type" => "task" ] "previous" => array:2 [ "refs" => "1434946" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1184 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1186 #items: array:1 [ 0 => App\Models\BookPage {#1154 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1435682 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "47" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-47" "field_display_title" => "47" "field_folder" => "3" "field_image_name" => "47" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Branch {#1168 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" 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#visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Element {#1115 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1699069 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => 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[] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1435683" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435681" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:2 [ 0 => App\Models\Task {#1111 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1435310 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "47" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/48-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } 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№7 (с. 47)
Условие. №7 (с. 47)
скриншот условия
7. Изобразите на окружностях (рис. 37) положения точечных тел, законы движения которых приведены в задании 6, в моменты времени $\text{t}$, равные 0, 1, 2 и 3 с. Угол $\phi$ отсчитывайте от оси $\text{X}$ против хода часовой стрелки, если он положителен, и по ходу часовой стрелки, если он отрицателен.
Рис. 37
Решение. №7 (с. 47)
Дано:
Законы движения точечных тел (из задания 6):
а) $\phi(t) = \frac{\pi}{2} t$
б) $\phi(t) = \pi(1-t)$
в) $\phi(t) = -\frac{\pi}{4} t$
г) $\phi(t) = \frac{\pi}{4} + \frac{\pi}{2} t$
д) $\phi(t) = \frac{\pi}{2} - \frac{\pi}{4} t$
Моменты времени: $t_0 = 0$ с, $t_1 = 1$ с, $t_2 = 2$ с, $t_3 = 3$ с.
Найти:
Положения точечных тел $\phi$ в заданные моменты времени.
Решение:
Для каждого закона движения рассчитаем угловое положение $\phi$ в моменты времени $t = 0, 1, 2, 3$ с. Согласно условию, положительные углы отсчитываются от оси Х против часовой стрелки, а отрицательные — по часовой стрелке.
а)
Закон движения: $\phi(t) = \frac{\pi}{2} t$.
При $t = 0$ с: $\phi = \frac{\pi}{2} \cdot 0 = 0$ рад. Положение на положительной части оси Х.
При $t = 1$ с: $\phi = \frac{\pi}{2} \cdot 1 = \frac{\pi}{2}$ рад ($90^\circ$). Положение на положительной части оси Y.
При $t = 2$ с: $\phi = \frac{\pi}{2} \cdot 2 = \pi$ рад ($180^\circ$). Положение на отрицательной части оси Х.
При $t = 3$ с: $\phi = \frac{\pi}{2} \cdot 3 = \frac{3\pi}{2}$ рад ($270^\circ$). Положение на отрицательной части оси Y.
Ответ: В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $0$, $\frac{\pi}{2}$, $\pi$ и $\frac{3\pi}{2}$ радиан, отсчитанным против часовой стрелки от положительного направления оси Х.
б)
Закон движения: $\phi(t) = \pi(1-t) = \pi - \pi t$.
При $t = 0$ с: $\phi = \pi(1-0) = \pi$ рад ($180^\circ$). Положение на отрицательной части оси Х.
При $t = 1$ с: $\phi = \pi(1-1) = 0$ рад. Положение на положительной части оси Х.
При $t = 2$ с: $\phi = \pi(1-2) = -\pi$ рад ($-180^\circ$). Угол отрицательный, отсчитывается по часовой стрелке. Положение совпадает с углом $\pi$, т.е. на отрицательной части оси Х.
При $t = 3$ с: $\phi = \pi(1-3) = -2\pi$ рад ($-360^\circ$). Угол отрицательный, отсчитывается по часовой стрелке. Положение совпадает с углом $0$, т.е. на положительной части оси Х.
Ответ: В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $\pi$, $0$, $-\pi$ (эквивалентно $\pi$), $-2\pi$ (эквивалентно $0$) радиан. Тело оказывается поочередно на отрицательной и положительной частях оси Х.
в)
Закон движения: $\phi(t) = -\frac{\pi}{4} t$.
При $t = 0$ с: $\phi = -\frac{\pi}{4} \cdot 0 = 0$ рад. Положение на положительной части оси Х.
При $t = 1$ с: $\phi = -\frac{\pi}{4}$ рад ($-45^\circ$). Угол отсчитывается по часовой стрелке, положение на биссектрисе IV координатного угла.
При $t = 2$ с: $\phi = -\frac{\pi}{4} \cdot 2 = -\frac{\pi}{2}$ рад ($-90^\circ$). Угол отсчитывается по часовой стрелке. Положение на отрицательной части оси Y.
При $t = 3$ с: $\phi = -\frac{\pi}{4} \cdot 3 = -\frac{3\pi}{4}$ рад ($-135^\circ$). Угол отсчитывается по часовой стрелке, положение на биссектрисе III координатного угла.
Ответ: В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $0$, $-\frac{\pi}{4}$, $-\frac{\pi}{2}$ и $-\frac{3\pi}{4}$ радиан, отсчитанным по часовой стрелке (кроме $t=0$).
г)
Закон движения: $\phi(t) = \frac{\pi}{4} + \frac{\pi}{2} t$.
При $t = 0$ с: $\phi = \frac{\pi}{4} + \frac{\pi}{2} \cdot 0 = \frac{\pi}{4}$ рад ($45^\circ$). Положение на биссектрисе I координатного угла.
При $t = 1$ с: $\phi = \frac{\pi}{4} + \frac{\pi}{2} = \frac{3\pi}{4}$ рад ($135^\circ$). Положение на биссектрисе II координатного угла.
При $t = 2$ с: $\phi = \frac{\pi}{4} + \pi = \frac{5\pi}{4}$ рад ($225^\circ$). Положение на биссектрисе III координатного угла.
При $t = 3$ с: $\phi = \frac{\pi}{4} + \frac{3\pi}{2} = \frac{7\pi}{4}$ рад ($315^\circ$). Положение на биссектрисе IV координатного угла.
Ответ: В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $\frac{\pi}{4}$, $\frac{3\pi}{4}$, $\frac{5\pi}{4}$ и $\frac{7\pi}{4}$ радиан, отсчитанным против часовой стрелки.
д)
Закон движения: $\phi(t) = \frac{\pi}{2} - \frac{\pi}{4} t$.
При $t = 0$ с: $\phi = \frac{\pi}{2} - 0 = \frac{\pi}{2}$ рад ($90^\circ$). Положение на положительной части оси Y.
При $t = 1$ с: $\phi = \frac{\pi}{2} - \frac{\pi}{4} = \frac{\pi}{4}$ рад ($45^\circ$). Положение на биссектрисе I координатного угла.
При $t = 2$ с: $\phi = \frac{\pi}{2} - \frac{\pi}{2} = 0$ рад. Положение на положительной части оси Х.
При $t = 3$ с: $\phi = \frac{\pi}{2} - \frac{3\pi}{4} = -\frac{\pi}{4}$ рад ($-45^\circ$). Угол отсчитывается по часовой стрелке, положение на биссектрисе IV координатного угла.
Ответ: В моменты времени 0, 1, 2, 3 с тело последовательно находится в точках, соответствующих углам $\frac{\pi}{2}$, $\frac{\pi}{4}$, $0$ и $-\frac{\pi}{4}$ радиан.
Другие задания:
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