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Номер 4, страница 71 - гдз по физике 9 класс учебник Изергин
Авторы: Изергин Э. Т.
Тип: Учебник
Серия: инновационная школа
Издательство: Русское слово
Год издания: 2019 - 2026
Цвет обложки: синий
ISBN: 978-5-533-01069-6
Популярные ГДЗ в 9 классе
Глава III. Механические колебания и волны. Параграф 14. Равномерное движение по окружности - номер 4, страница 71.
App\Models\Task {#1024 // 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" => 1439731 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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" => 1439560 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #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" …2 ] "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 [ …6] "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" => "67" "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 {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #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" => 4169 "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 {#1034 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1036 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1040 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4169 "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 {#1034 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1036 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1040 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1062 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1439560 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "67" "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 {#1030} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1062} ] #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 {#1063 #items: array:2 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1064 #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" => 1439561 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Равномерное движение по окружности" "field_branch_order" => "14" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:1 [ 0 => App\Models\Term {#1066 #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 [ …6] "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 [ …6] "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" => "67" "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 {#1067 #items: array:1 [ 0 => App\Models\Book {#1068 #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" => 4169 "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 {#1069 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1073 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1075 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1077 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4169 "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 {#1069 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1073 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1075 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1077 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1097 #items: array:1 [ 0 => App\Models\Branch {#1098 #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" => 1439560 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_page_start" => "67" "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 {#1101 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1102 …2} ] #original: array:24 [ "id" => 1439560 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические колебания и волны" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_page_start" => "67" "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 {#1101 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1102 …2} ] #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" => 1439561 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Равномерное движение по окружности" "field_branch_order" => "14" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065} "field_page_start" => "67" "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 {#1067} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1097} ] #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 {#1103 #items: array:2 [ 0 => App\Models\Element {#1104 #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" => 1707278 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ 0 => App\Models\Edition {#1106 #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" => 6139 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1109 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1111 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6139 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1109 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1111 …2} "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" => "1439731" "type" => "task" ] "text" => "<p><strong>4.</strong> Для каждого из наблюдаемых явлений, описанных в начале параграфа, укажите, если это возможно, период, частоту, угловую и линейную скорости.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1421" "height" => 236 "path" => "/media/fizika_09/izergin-u/0-14/4-1.webp?ts=1759529221" ] ] ] #original: array:7 [ "id" => 1707278 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1105} "task" => array:2 [ "refs" => "1439731" "type" => "task" ] "text" => "<p><strong>4.</strong> Для каждого из наблюдаемых явлений, описанных в начале параграфа, укажите, если это возможно, период, частоту, угловую и линейную скорости.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1421" "height" => 236 "path" => "/media/fizika_09/izergin-u/0-14/4-1.webp?ts=1759529221" ] ] ] #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 {#1112 #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" => 1813296 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:1 [ 0 => App\Models\Edition {#1114 #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" => 6646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "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 {#1117 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "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 {#1117 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1119 …2} "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" => "1439731" "type" => "task" ] "text" => "<p>Поскольку в задании не указаны конкретные явления, описанные в начале параграфа, рассмотрим несколько стандартных примеров периодических движений.</p><p><strong>Вращение Земли вокруг своей оси</strong></p><p>Это периодическое движение.<br><em>Период (T)</em> - время одного полного оборота. Для Земли это звёздные сутки. $T \approx 23 \text{ ч } 56 \text{ мин } 4 \text{ с} = 86164 \text{ с}$. Часто для упрощения принимают $T = 24 \text{ ч} = 86400 \text{ с}$.<br><em>Частота (ν)</em> - число оборотов в единицу времени. Она связана с периодом соотношением $\nu = 1/T$. Для Земли $\nu = 1 / 86164 \text{ с} \approx 1.16 \times 10^{-5} \text{ Гц}$.<br><em>Угловая скорость (ω)</em> - скорость изменения угла поворота. Она связана с периодом как $\omega = 2\pi/T$. Для Земли $\omega = 2\pi / 86164 \text{ с} \approx 7.29 \times 10^{-5} \text{ рад/с}$. Эта величина одинакова для всех точек на Земле (кроме точек на оси вращения).<br><em>Линейная скорость (v)</em> - скорость движения точки. Она зависит от расстояния до оси вращения $\text{R}$ по формуле $v = \omega R$. Для точки на поверхности Земли на географической широте $\phi$, расстояние до оси вращения равно $R = R_З \cos(\phi)$, где $R_З$ - радиус Земли. Таким образом, линейная скорость на экваторе ($\phi = 0^{\circ}$, $R \approx 6378$ км) максимальна и составляет $v \approx 465 \text{ м/с}$, а на полюсах ($\phi = 90^{\circ}$, $R = 0$) равна нулю. Указать единое значение линейной скорости для всего явления невозможно.</p><p><strong>Ответ:</strong> Период $T \approx 86164 \text{ с}$, частота $\nu \approx 1.16 \times 10^{-5} \text{ Гц}$, угловая скорость $\omega \approx 7.29 \times 10^{-5} \text{ рад/с}$. Линейная скорость $\text{v}$ зависит от широты и изменяется от $\text{0}$ на полюсах до примерно $465 \text{ м/с}$ на экваторе.</p><p><strong>Обращение Земли вокруг Солнца</strong></p><p>Это периодическое движение.<br><em>Период (T)</em> - время одного полного оборота вокруг Солнца, что составляет один год. $T \approx 365.25 \text{ суток} \approx 3.156 \times 10^7 \text{ с}$.<br><em>Частота (ν)</em> - $\nu = 1/T = 1 / (3.156 \times 10^7 \text{ с}) \approx 3.17 \times 10^{-8} \text{ Гц}$.<br><em>Угловая скорость (ω)</em> - Поскольку орбита Земли — эллипс, угловая скорость не является постоянной. Однако можно рассчитать среднюю угловую скорость: $\omega_{ср} = 2\pi/T = 2\pi / (3.156 \times 10^7 \text{ с}) \approx 1.99 \times 10^{-7} \text{ рад/с}$.<br><em>Линейная скорость (v)</em> - также не является постоянной из-за эллиптической орбиты (согласно второму закону Кеплера). Она максимальна в перигелии и минимальна в афелии. Средняя линейная скорость может быть найдена как $v_{ср} = \omega_{ср} R_{ср}$, где $R_{ср}$ - средний радиус орбиты (около $1.496 \times 10^{11} \text{ м}$). $v_{ср} \approx (1.99 \times 10^{-7} \text{ рад/с}) \times (1.496 \times 10^{11} \text{ м}) \approx 29.8 \text{ км/с}$.</p><p><strong>Ответ:</strong> Период $T \approx 3.156 \times 10^7 \text{ с}$, частота $\nu \approx 3.17 \times 10^{-8} \text{ Гц}$. Средняя угловая скорость $\omega_{ср} \approx 1.99 \times 10^{-7} \text{ рад/с}$, средняя линейная скорость $v_{ср} \approx 29.8 \text{ км/с}$. Мгновенные значения угловой и линейной скоростей непостоянны.</p><p><strong>Движение секундной стрелки часов</strong></p><p>Это пример равномерного вращательного движения.<br><em>Период (T)</em> - время одного полного оборота. $T = 60 \text{ с}$.<br><em>Частота (ν)</em> - $\nu = 1/T = 1/60 \text{ Гц}$.<br><em>Угловая скорость (ω)</em> - постоянна для всех точек стрелки. $\omega = 2\pi/T = 2\pi/60 = \pi/30 \text{ рад/с} \approx 0.105 \text{ рад/с}$.<br><em>Линейная скорость (v)</em> - зависит от расстояния $\text{r}$ от центра вращения: $v = \omega r = (\pi/30)r$. Линейная скорость равна нулю в точке крепления стрелки и максимальна на её конце. Поэтому указать единое значение для всей стрелки невозможно.</p><p><strong>Ответ:</strong> Период $T = 60 \text{ с}$, частота $\nu = 1/60 \text{ Гц}$, угловая скорость $\omega = \pi/30 \text{ рад/с}$. Линейная скорость $\text{v}$ пропорциональна расстоянию от центра вращения ($v = (\pi/30)r$).</p><p><strong>Движение минутной стрелки часов</strong></p><p>Это пример равномерного вращательного движения.<br><em>Период (T)</em> - время одного полного оборота. $T = 60 \text{ мин} = 3600 \text{ с}$.<br><em>Частота (ν)</em> - $\nu = 1/T = 1/3600 \text{ Гц}$.<br><em>Угловая скорость (ω)</em> - постоянна для всех точек стрелки. $\omega = 2\pi/T = 2\pi/3600 = \pi/1800 \text{ рад/с}$.<br><em>Линейная скорость (v)</em> - зависит от расстояния $\text{r}$ от центра вращения: $v = \omega r = (\pi/1800)r$. Линейная скорость равна нулю в точке крепления стрелки и максимальна на её конце.</p><p><strong>Ответ:</strong> Период $T = 3600 \text{ с}$, частота $\nu = 1/3600 \text{ Гц}$, угловая скорость $\omega = \pi/1800 \text{ рад/с}$. Линейная скорость $\text{v}$ пропорциональна расстоянию от центра вращения ($v = (\pi/1800)r$).</p><p><strong>Движение часовой стрелки часов</strong></p><p>Это пример равномерного вращательного движения.<br><em>Период (T)</em> - время одного полного оборота (на стандартном циферблате). $T = 12 \text{ ч} = 12 \times 3600 \text{ с} = 43200 \text{ с}$.<br><em>Частота (ν)</em> - $\nu = 1/T = 1/43200 \text{ Гц}$.<br><em>Угловая скорость (ω)</em> - постоянна для всех точек стрелки. $\omega = 2\pi/T = 2\pi/43200 = \pi/21600 \text{ рад/с}$.<br><em>Линейная скорость (v)</em> - зависит от расстояния $\text{r}$ от центра вращения: $v = \omega r = (\pi/21600)r$. Линейная скорость равна нулю в точке крепления стрелки и максимальна на её конце.</p><p><strong>Ответ:</strong> Период $T = 43200 \text{ с}$, частота $\nu = 1/43200 \text{ Гц}$, угловая скорость $\omega = \pi/21600 \text{ рад/с}$. Линейная скорость $\text{v}$ пропорциональна расстоянию от центра вращения ($v = (\pi/21600)r$).</p>" ] #original: array:6 [ "id" => 1813296 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1113} "task" => array:2 [ "refs" => "1439731" "type" => "task" ] "text" => "<p>Поскольку в задании не указаны конкретные явления, описанные в начале параграфа, рассмотрим несколько стандартных примеров периодических движений.</p><p><strong>Вращение Земли вокруг своей оси</strong></p><p>Это периодическое движение.<br><em>Период (T)</em> - время одного полного оборота. Для Земли это звёздные сутки. $T \approx 23 \text{ ч } 56 \text{ мин } 4 \text{ с} = 86164 \text{ с}$. Часто для упрощения принимают $T = 24 \text{ ч} = 86400 \text{ с}$.<br><em>Частота (ν)</em> - число оборотов в единицу времени. Она связана с периодом соотношением $\nu = 1/T$. Для Земли $\nu = 1 / 86164 \text{ с} \approx 1.16 \times 10^{-5} \text{ Гц}$.<br><em>Угловая скорость (ω)</em> - скорость изменения угла поворота. Она связана с периодом как $\omega = 2\pi/T$. Для Земли $\omega = 2\pi / 86164 \text{ с} \approx 7.29 \times 10^{-5} \text{ рад/с}$. Эта величина одинакова для всех точек на Земле (кроме точек на оси вращения).<br><em>Линейная скорость (v)</em> - скорость движения точки. Она зависит от расстояния до оси вращения $\text{R}$ по формуле $v = \omega R$. Для точки на поверхности Земли на географической широте $\phi$, расстояние до оси вращения равно $R = R_З \cos(\phi)$, где $R_З$ - радиус Земли. Таким образом, линейная скорость на экваторе ($\phi = 0^{\circ}$, $R \approx 6378$ км) максимальна и составляет $v \approx 465 \text{ м/с}$, а на полюсах ($\phi = 90^{\circ}$, $R = 0$) равна нулю. Указать единое значение линейной скорости для всего явления невозможно.</p><p><strong>Ответ:</strong> Период $T \approx 86164 \text{ с}$, частота $\nu \approx 1.16 \times 10^{-5} \text{ Гц}$, угловая скорость $\omega \approx 7.29 \times 10^{-5} \text{ рад/с}$. Линейная скорость $\text{v}$ зависит от широты и изменяется от $\text{0}$ на полюсах до примерно $465 \text{ м/с}$ на экваторе.</p><p><strong>Обращение Земли вокруг Солнца</strong></p><p>Это периодическое движение.<br><em>Период (T)</em> - время одного полного оборота вокруг Солнца, что составляет один год. $T \approx 365.25 \text{ суток} \approx 3.156 \times 10^7 \text{ с}$.<br><em>Частота (ν)</em> - $\nu = 1/T = 1 / (3.156 \times 10^7 \text{ с}) \approx 3.17 \times 10^{-8} \text{ Гц}$.<br><em>Угловая скорость (ω)</em> - Поскольку орбита Земли — эллипс, угловая скорость не является постоянной. Однако можно рассчитать среднюю угловую скорость: $\omega_{ср} = 2\pi/T = 2\pi / (3.156 \times 10^7 \text{ с}) \approx 1.99 \times 10^{-7} \text{ рад/с}$.<br><em>Линейная скорость (v)</em> - также не является постоянной из-за эллиптической орбиты (согласно второму закону Кеплера). Она максимальна в перигелии и минимальна в афелии. Средняя линейная скорость может быть найдена как $v_{ср} = \omega_{ср} R_{ср}$, где $R_{ср}$ - средний радиус орбиты (около $1.496 \times 10^{11} \text{ м}$). $v_{ср} \approx (1.99 \times 10^{-7} \text{ рад/с}) \times (1.496 \times 10^{11} \text{ м}) \approx 29.8 \text{ км/с}$.</p><p><strong>Ответ:</strong> Период $T \approx 3.156 \times 10^7 \text{ с}$, частота $\nu \approx 3.17 \times 10^{-8} \text{ Гц}$. Средняя угловая скорость $\omega_{ср} \approx 1.99 \times 10^{-7} \text{ рад/с}$, средняя линейная скорость $v_{ср} \approx 29.8 \text{ км/с}$. Мгновенные значения угловой и линейной скоростей непостоянны.</p><p><strong>Движение секундной стрелки часов</strong></p><p>Это пример равномерного вращательного движения.<br><em>Период (T)</em> - время одного полного оборота. $T = 60 \text{ с}$.<br><em>Частота (ν)</em> - $\nu = 1/T = 1/60 \text{ Гц}$.<br><em>Угловая скорость (ω)</em> - постоянна для всех точек стрелки. $\omega = 2\pi/T = 2\pi/60 = \pi/30 \text{ рад/с} \approx 0.105 \text{ рад/с}$.<br><em>Линейная скорость (v)</em> - зависит от расстояния $\text{r}$ от центра вращения: $v = \omega r = (\pi/30)r$. Линейная скорость равна нулю в точке крепления стрелки и максимальна на её конце. Поэтому указать единое значение для всей стрелки невозможно.</p><p><strong>Ответ:</strong> Период $T = 60 \text{ с}$, частота $\nu = 1/60 \text{ Гц}$, угловая скорость $\omega = \pi/30 \text{ рад/с}$. Линейная скорость $\text{v}$ пропорциональна расстоянию от центра вращения ($v = (\pi/30)r$).</p><p><strong>Движение минутной стрелки часов</strong></p><p>Это пример равномерного вращательного движения.<br><em>Период (T)</em> - время одного полного оборота. $T = 60 \text{ мин} = 3600 \text{ с}$.<br><em>Частота (ν)</em> - $\nu = 1/T = 1/3600 \text{ Гц}$.<br><em>Угловая скорость (ω)</em> - постоянна для всех точек стрелки. $\omega = 2\pi/T = 2\pi/3600 = \pi/1800 \text{ рад/с}$.<br><em>Линейная скорость (v)</em> - зависит от расстояния $\text{r}$ от центра вращения: $v = \omega r = (\pi/1800)r$. Линейная скорость равна нулю в точке крепления стрелки и максимальна на её конце.</p><p><strong>Ответ:</strong> Период $T = 3600 \text{ с}$, частота $\nu = 1/3600 \text{ Гц}$, угловая скорость $\omega = \pi/1800 \text{ рад/с}$. Линейная скорость $\text{v}$ пропорциональна расстоянию от центра вращения ($v = (\pi/1800)r$).</p><p><strong>Движение часовой стрелки часов</strong></p><p>Это пример равномерного вращательного движения.<br><em>Период (T)</em> - время одного полного оборота (на стандартном циферблате). $T = 12 \text{ ч} = 12 \times 3600 \text{ с} = 43200 \text{ с}$.<br><em>Частота (ν)</em> - $\nu = 1/T = 1/43200 \text{ Гц}$.<br><em>Угловая скорость (ω)</em> - постоянна для всех точек стрелки. $\omega = 2\pi/T = 2\pi/43200 = \pi/21600 \text{ рад/с}$.<br><em>Линейная скорость (v)</em> - зависит от расстояния $\text{r}$ от центра вращения: $v = \omega r = (\pi/21600)r$. Линейная скорость равна нулю в точке крепления стрелки и максимальна на её конце.</p><p><strong>Ответ:</strong> Период $T = 43200 \text{ с}$, частота $\nu = 1/43200 \text{ Гц}$, угловая скорость $\omega = \pi/21600 \text{ рад/с}$. Линейная скорость $\text{v}$ пропорциональна расстоянию от центра вращения ($v = (\pi/21600)r$).</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" => "1439732" "type" => "task" ] "previous" => array:2 [ "refs" => "1439730" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:1 [ 0 => App\Models\Book {#1121 #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" => 4169 "created_at" => "2026-04-10 13:58:26" "updated_at" => null 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"field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ 0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" "alt" => "" "width" => "1881" "height" => "2502" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1145} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148} "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 } "page" => Illuminate\Database\Eloquent\Collection {#1439 #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" => 1439389 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_url" => "/9-klass/fizika/izergin-uchebnik/page-71" "field_display_title" => "71" "field_folder" => "1" "field_image_name" => "71" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1157 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:1 [ 0 => App\Models\Book {#1158 #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" => 4169 "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 {#1159 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1168 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1182 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1183 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1184 …2} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4169 "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 {#1159 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1168 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1182 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1183 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1184 …2} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 "edition_groups" => Illuminate\Database\Eloquent\Collection {#1187 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1188 #items: array:1 [ 0 => App\Models\Element {#1189 #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" => 1707627 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1190 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1707627 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1190 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #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" => "1439390" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1439388" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1197 #items: array:7 [ 0 => App\Models\Task {#1198 #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" => 1439728 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1199 …2} "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 {#1201 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1202 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1237 …2} "content" => Illuminate\Database\Eloquent\Collection {#1311 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1322 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1439728 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1199 …2} "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 {#1201 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1202 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1237 …2} "content" => Illuminate\Database\Eloquent\Collection {#1311 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1322 …2} "page" => array:2 [ …2] ] #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\Task {#1323 #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" => 1439729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1324 …2} "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 {#1325 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1326 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1327 …2} "content" => Illuminate\Database\Eloquent\Collection {#1328 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1333 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1439729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1324 …2} "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 {#1325 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1326 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1327 …2} "content" => Illuminate\Database\Eloquent\Collection {#1328 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1333 …2} "page" => array:2 [ …2] ] #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\Task {#1334 #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" => 1439730 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1335 …2} "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 {#1336 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1337 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1338 …2} "content" => Illuminate\Database\Eloquent\Collection {#1339 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1356 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1439730 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1335 …2} "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 {#1336 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1337 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1338 …2} "content" => Illuminate\Database\Eloquent\Collection {#1339 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1356 …2} "page" => array:2 [ …2] ] #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\Task {#1357 #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" => 1439731 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1358 …2} "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 {#1359 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1360 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1361 …2} "content" => Illuminate\Database\Eloquent\Collection {#1362 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1379 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1439731 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1358 …2} "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 {#1359 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1360 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1361 …2} "content" => Illuminate\Database\Eloquent\Collection {#1362 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1379 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1380 #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" => 1439732 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1381 …2} "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 {#1382 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1383 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1384 …2} "content" => Illuminate\Database\Eloquent\Collection {#1385 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1402 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1439732 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "71" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/14-5" "field_display_title" => "5" "field_outside_task" 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№4 (с. 71)
Условие. №4 (с. 71)
скриншот условия
4. Для каждого из наблюдаемых явлений, описанных в начале параграфа, укажите, если это возможно, период, частоту, угловую и линейную скорости.
Решение. №4 (с. 71)
Поскольку в задании не указаны конкретные явления, описанные в начале параграфа, рассмотрим несколько стандартных примеров периодических движений.
Вращение Земли вокруг своей оси
Это периодическое движение.
Период (T) - время одного полного оборота. Для Земли это звёздные сутки. $T \approx 23 \text{ ч } 56 \text{ мин } 4 \text{ с} = 86164 \text{ с}$. Часто для упрощения принимают $T = 24 \text{ ч} = 86400 \text{ с}$.
Частота (ν) - число оборотов в единицу времени. Она связана с периодом соотношением $\nu = 1/T$. Для Земли $\nu = 1 / 86164 \text{ с} \approx 1.16 \times 10^{-5} \text{ Гц}$.
Угловая скорость (ω) - скорость изменения угла поворота. Она связана с периодом как $\omega = 2\pi/T$. Для Земли $\omega = 2\pi / 86164 \text{ с} \approx 7.29 \times 10^{-5} \text{ рад/с}$. Эта величина одинакова для всех точек на Земле (кроме точек на оси вращения).
Линейная скорость (v) - скорость движения точки. Она зависит от расстояния до оси вращения $\text{R}$ по формуле $v = \omega R$. Для точки на поверхности Земли на географической широте $\phi$, расстояние до оси вращения равно $R = R_З \cos(\phi)$, где $R_З$ - радиус Земли. Таким образом, линейная скорость на экваторе ($\phi = 0^{\circ}$, $R \approx 6378$ км) максимальна и составляет $v \approx 465 \text{ м/с}$, а на полюсах ($\phi = 90^{\circ}$, $R = 0$) равна нулю. Указать единое значение линейной скорости для всего явления невозможно.
Ответ: Период $T \approx 86164 \text{ с}$, частота $\nu \approx 1.16 \times 10^{-5} \text{ Гц}$, угловая скорость $\omega \approx 7.29 \times 10^{-5} \text{ рад/с}$. Линейная скорость $\text{v}$ зависит от широты и изменяется от $\text{0}$ на полюсах до примерно $465 \text{ м/с}$ на экваторе.
Обращение Земли вокруг Солнца
Это периодическое движение.
Период (T) - время одного полного оборота вокруг Солнца, что составляет один год. $T \approx 365.25 \text{ суток} \approx 3.156 \times 10^7 \text{ с}$.
Частота (ν) - $\nu = 1/T = 1 / (3.156 \times 10^7 \text{ с}) \approx 3.17 \times 10^{-8} \text{ Гц}$.
Угловая скорость (ω) - Поскольку орбита Земли — эллипс, угловая скорость не является постоянной. Однако можно рассчитать среднюю угловую скорость: $\omega_{ср} = 2\pi/T = 2\pi / (3.156 \times 10^7 \text{ с}) \approx 1.99 \times 10^{-7} \text{ рад/с}$.
Линейная скорость (v) - также не является постоянной из-за эллиптической орбиты (согласно второму закону Кеплера). Она максимальна в перигелии и минимальна в афелии. Средняя линейная скорость может быть найдена как $v_{ср} = \omega_{ср} R_{ср}$, где $R_{ср}$ - средний радиус орбиты (около $1.496 \times 10^{11} \text{ м}$). $v_{ср} \approx (1.99 \times 10^{-7} \text{ рад/с}) \times (1.496 \times 10^{11} \text{ м}) \approx 29.8 \text{ км/с}$.
Ответ: Период $T \approx 3.156 \times 10^7 \text{ с}$, частота $\nu \approx 3.17 \times 10^{-8} \text{ Гц}$. Средняя угловая скорость $\omega_{ср} \approx 1.99 \times 10^{-7} \text{ рад/с}$, средняя линейная скорость $v_{ср} \approx 29.8 \text{ км/с}$. Мгновенные значения угловой и линейной скоростей непостоянны.
Движение секундной стрелки часов
Это пример равномерного вращательного движения.
Период (T) - время одного полного оборота. $T = 60 \text{ с}$.
Частота (ν) - $\nu = 1/T = 1/60 \text{ Гц}$.
Угловая скорость (ω) - постоянна для всех точек стрелки. $\omega = 2\pi/T = 2\pi/60 = \pi/30 \text{ рад/с} \approx 0.105 \text{ рад/с}$.
Линейная скорость (v) - зависит от расстояния $\text{r}$ от центра вращения: $v = \omega r = (\pi/30)r$. Линейная скорость равна нулю в точке крепления стрелки и максимальна на её конце. Поэтому указать единое значение для всей стрелки невозможно.
Ответ: Период $T = 60 \text{ с}$, частота $\nu = 1/60 \text{ Гц}$, угловая скорость $\omega = \pi/30 \text{ рад/с}$. Линейная скорость $\text{v}$ пропорциональна расстоянию от центра вращения ($v = (\pi/30)r$).
Движение минутной стрелки часов
Это пример равномерного вращательного движения.
Период (T) - время одного полного оборота. $T = 60 \text{ мин} = 3600 \text{ с}$.
Частота (ν) - $\nu = 1/T = 1/3600 \text{ Гц}$.
Угловая скорость (ω) - постоянна для всех точек стрелки. $\omega = 2\pi/T = 2\pi/3600 = \pi/1800 \text{ рад/с}$.
Линейная скорость (v) - зависит от расстояния $\text{r}$ от центра вращения: $v = \omega r = (\pi/1800)r$. Линейная скорость равна нулю в точке крепления стрелки и максимальна на её конце.
Ответ: Период $T = 3600 \text{ с}$, частота $\nu = 1/3600 \text{ Гц}$, угловая скорость $\omega = \pi/1800 \text{ рад/с}$. Линейная скорость $\text{v}$ пропорциональна расстоянию от центра вращения ($v = (\pi/1800)r$).
Движение часовой стрелки часов
Это пример равномерного вращательного движения.
Период (T) - время одного полного оборота (на стандартном циферблате). $T = 12 \text{ ч} = 12 \times 3600 \text{ с} = 43200 \text{ с}$.
Частота (ν) - $\nu = 1/T = 1/43200 \text{ Гц}$.
Угловая скорость (ω) - постоянна для всех точек стрелки. $\omega = 2\pi/T = 2\pi/43200 = \pi/21600 \text{ рад/с}$.
Линейная скорость (v) - зависит от расстояния $\text{r}$ от центра вращения: $v = \omega r = (\pi/21600)r$. Линейная скорость равна нулю в точке крепления стрелки и максимальна на её конце.
Ответ: Период $T = 43200 \text{ с}$, частота $\nu = 1/43200 \text{ Гц}$, угловая скорость $\omega = \pi/21600 \text{ рад/с}$. Линейная скорость $\text{v}$ пропорциональна расстоянию от центра вращения ($v = (\pi/21600)r$).
Другие задания:
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