| 1. |
info: 2025-04-26 01:27:28.260 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
75ms [Parameters=[@p7='5726b745-56fb-4bf2-a276-c5abd51b4d8c', @p0='True', @p1='False', @p2='0', @p3='b82e3933-e7f4-4f2b-a8dc-e8a290222f2a', @p4='82.jpg' (Size = 100), @p5='https://knowledgenest.blob.core.windows.net/scanners/0/[Fizika][Fizika 11–12 klasės][Vadovėlis (Judėjimas ir jėgos) -- 1157]/pages/82.jpg' (Size = 1000), @p6='## 3.2*. Apskritimu judančio kūno poslinkis ir greitis
### Apskritimu judančio kūno poslinkis
Poslinkiu vadinama kryptinė atkarpa, jungianti pradinę kūno padėtį su galine jo padėtimi. Tiesiai judančio kūno poslinkio ir greičio kryptys sutampa. O kokia yra šių vektorių kryptis, kai kūnas juda kreive?
Pirma nustatykime apskritimu judančio kūno poslinkio kryptį. Tarkime, kad kūnas kreive pasislinko iš taško A į tašką B. Tada jo nueitas kelias yra lanko AB ilgis, o poslinkis – vektorius $\vec{s}$, nukreiptas išilgai stygos AB. Taigi apskritimu judančio kūno poslinkis nukreiptas styga.
### Apskritimu judančio kūno linijinis greitis
Išsiaiškinkime, kaip nukreiptas apskritimu judančio kūno greitis. Jo kryptis šiuo atveju jau nebesutampa su poslinkio AB kryptimi. Judėjimą lanku AB padalykime į trumpesnius laiko tarpus. Kūno poslinkius per juos ($\vec{s}_1$, $\vec{s}_2$, $\vec{s}_3$) pavaizduokime trumpesnėmis stygomis. Įsivaizduokime, kad kūnas juda gauta laužte. Dabar kūno judėjimas kiekviena jos grandimi yra tiesiaeigis, todėl greičio vektorius $\vec{v}$ nukreiptas išilgai poslinkio vektoriaus. Trumpinant tiesius ruoželius (stygas), laužtė bus vis panašesnė į glodžią kreivę, kol galiausiai su ja sutaps. Kūno greitis kiekviename šios kreivės taške yra momentinis greitis. Jis nukreiptas per tą tašką einančia kreivės liestine.
Apskritimu judančio kūno momentinis greitis vadinamas linijiniu greičiu. Vadinasi, apskritimu judančio kūno linijinis greitis bet kuriame trajektorijos taške yra nukreiptas apskritimo liestine, einančia per tą tašką. Tai patvirtina ir aplinkoje stebimi reiškiniai. Pavyzdžiui, liestine lekia smėlis nuo buksuojančio keturračio motociklo ratų, kibirkštys nuo galąstuvo disko.
' (Size = 4000)], CommandType='Text', CommandTimeout='30']
SET IMPLICIT_TRANSACTIONS OFF;
SET NOCOUNT ON;
UPDATE [ScannerPages] SET [Active] = @p0, [Deleted] = @p1, [Position] = @p2, [ScannerId] = @p3, [StorageMediaName] = @p4, [StorageMediaUrl] = @p5, [Text] = @p6
OUTPUT 1
WHERE [Id] = @p7;
|
| 2. |
info: 2025-04-26 01:27:29.531 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
2ms [Parameters=[@__id_0='293fa425-4ae3-34b3-4b22-9d091fec9347', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [c].[Id], [c].[Active], [c].[Deleted], [c].[Description], [c].[DescriptionBackup], [c].[Left], [c].[ParentId], [c].[Position], [c].[ProcessorGenerateImagePrompt], [c].[Right], [c].[SiteId], [c].[StorageMediaName], [c].[StorageMediaUrl], [c].[Title], [c].[TitleBackup], [c].[TitleSlug], [c].[TotalChildren], [c].[TotalScanners], [c].[TotalYoutubeVideos]
FROM [Categories] AS [c] WITH (NOLOCK)
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id]
|
| 3. |
info: 2025-04-26 01:27:29.562 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
30ms [Parameters=[@__id_0='293fa425-4ae3-34b3-4b22-9d091fec9347', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [c4].[Id], [c4].[Active], [c4].[Deleted], [c4].[Description], [c4].[DescriptionBackup], [c4].[Left], [c4].[ParentId], [c4].[Position], [c4].[ProcessorGenerateImagePrompt], [c4].[Right], [c4].[SiteId], [c4].[StorageMediaName], [c4].[StorageMediaUrl], [c4].[Title], [c4].[TitleBackup], [c4].[TitleSlug], [c4].[TotalChildren], [c4].[TotalScanners], [c4].[TotalYoutubeVideos], [c].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c0].[Id], [c0].[Active], [c0].[Deleted], [c0].[Description], [c0].[DescriptionBackup], [c0].[Left], [c0].[ParentId], [c0].[Position], [c0].[ProcessorGenerateImagePrompt], [c0].[Right], [c0].[SiteId], [c0].[StorageMediaName], [c0].[StorageMediaUrl], [c0].[Title], [c0].[TitleBackup], [c0].[TitleSlug], [c0].[TotalChildren], [c0].[TotalScanners], [c0].[TotalYoutubeVideos]
FROM [Categories] AS [c0] WITH (NOLOCK)
WHERE [c0].[Active] = CAST(1 AS bit) AND [c0].[Deleted] = CAST(0 AS bit)
) AS [c4] ON [c].[Id] = [c4].[ParentId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [c4].[Position], [c4].[Id]
|
| 4. |
info: 2025-04-26 01:27:29.572 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
2ms [Parameters=[@__id_0='293fa425-4ae3-34b3-4b22-9d091fec9347', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [c5].[Id], [c5].[Active], [c5].[Deleted], [c5].[Description], [c5].[DescriptionBackup], [c5].[Left], [c5].[ParentId], [c5].[Position], [c5].[ProcessorGenerateImagePrompt], [c5].[Right], [c5].[SiteId], [c5].[StorageMediaName], [c5].[StorageMediaUrl], [c5].[Title], [c5].[TitleBackup], [c5].[TitleSlug], [c5].[TotalChildren], [c5].[TotalScanners], [c5].[TotalYoutubeVideos], [c].[Id], [c4].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c0].[Id], [c0].[ParentId], [c0].[Position]
FROM [Categories] AS [c0] WITH (NOLOCK)
WHERE [c0].[Active] = CAST(1 AS bit) AND [c0].[Deleted] = CAST(0 AS bit)
) AS [c4] ON [c].[Id] = [c4].[ParentId]
INNER JOIN (
SELECT [c1].[Id], [c1].[Active], [c1].[Deleted], [c1].[Description], [c1].[DescriptionBackup], [c1].[Left], [c1].[ParentId], [c1].[Position], [c1].[ProcessorGenerateImagePrompt], [c1].[Right], [c1].[SiteId], [c1].[StorageMediaName], [c1].[StorageMediaUrl], [c1].[Title], [c1].[TitleBackup], [c1].[TitleSlug], [c1].[TotalChildren], [c1].[TotalScanners], [c1].[TotalYoutubeVideos]
FROM [Categories] AS [c1] WITH (NOLOCK)
WHERE [c1].[Active] = CAST(1 AS bit) AND [c1].[Deleted] = CAST(0 AS bit)
) AS [c5] ON [c4].[Id] = [c5].[ParentId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [c4].[Position], [c4].[Id], [c5].[Position]
|
| 5. |
info: 2025-04-26 01:27:29.639 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
66ms [Parameters=[@__id_0='293fa425-4ae3-34b3-4b22-9d091fec9347', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [s3].[ScannerId], [s3].[CategoryId], [s3].[Id], [s3].[Active], [s3].[CheatSheet], [s3].[CheatSheet2], [s3].[Deleted], [s3].[FactErrors], [s3].[FactErrorsExplanation], [s3].[ParentCategory2Id], [s3].[ParentCategoryId], [s3].[ProcessorGenerateImagePrompt], [s3].[Prompt], [s3].[Reference], [s3].[ReferenceSlug], [s3].[SiteId], [s3].[SpellingErrors], [s3].[SpellingErrorsExplanation], [s3].[Summary], [s3].[Title], [s3].[TitleBackup], [s3].[TitleSlug], [s3].[TotalCards], [s3].[TotalCards2], [s3].[TotalCategories], [s3].[TotalPages], [s3].[Verified], [c].[Id], [c4].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c0].[Id], [c0].[ParentId], [c0].[Position]
FROM [Categories] AS [c0] WITH (NOLOCK)
WHERE [c0].[Active] = CAST(1 AS bit) AND [c0].[Deleted] = CAST(0 AS bit)
) AS [c4] ON [c].[Id] = [c4].[ParentId]
INNER JOIN (
SELECT [c2].[ScannerId], [c2].[CategoryId], [s].[Id], [s].[Active], [s].[CheatSheet], [s].[CheatSheet2], [s].[Deleted], [s].[FactErrors], [s].[FactErrorsExplanation], [s].[ParentCategory2Id], [s].[ParentCategoryId], [s].[ProcessorGenerateImagePrompt], [s].[Prompt], [s].[Reference], [s].[ReferenceSlug], [s].[SiteId], [s].[SpellingErrors], [s].[SpellingErrorsExplanation], [s].[Summary], [s].[Title], [s].[TitleBackup], [s].[TitleSlug], [s].[TotalCards], [s].[TotalCards2], [s].[TotalCategories], [s].[TotalPages], [s].[Verified]
FROM [CategoryScanners] AS [c2]
INNER JOIN [Scanners] AS [s] ON [c2].[ScannerId] = [s].[Id]
WHERE [s].[Active] = CAST(1 AS bit) AND [s].[Deleted] = CAST(0 AS bit)
) AS [s3] ON [c4].[Id] = [s3].[CategoryId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [c4].[Position], [c4].[Id], [s3].[Id], [s3].[ScannerId], [s3].[CategoryId]
|
| 6. |
info: 2025-04-26 01:27:29.717 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
9ms [Parameters=[@__id_0='293fa425-4ae3-34b3-4b22-9d091fec9347', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [s4].[Id], [s4].[Active], [s4].[Context], [s4].[ContextBackup], [s4].[ContextStorageMediaName], [s4].[ContextStorageMediaUrl], [s4].[Deleted], [s4].[FactErrors], [s4].[FactErrorsExplanation], [s4].[Facts], [s4].[FactsBackup], [s4].[FactsStorageMediaName], [s4].[FactsStorageMediaUrl], [s4].[Position], [s4].[ProcessorGenerateImagePrompt], [s4].[Prompt], [s4].[ScannerId], [s4].[SpellingErrors], [s4].[SpellingErrorsExplanation], [s4].[StorageMediaName], [s4].[StorageMediaUrl], [s4].[Summary], [s4].[SummaryBackup], [s4].[SummaryStorageMediaName], [s4].[SummaryStorageMediaUrl], [s4].[Title], [s4].[TitleSlug], [s4].[TotalFillTheBlankSelectionQuestions], [s4].[TotalMultipleSelectionQuestions], [s4].[TotalOrderingQuestions], [s4].[TotalQuestionPoints], [s4].[TotalQuestions], [s4].[TotalShortAnswerQuestions], [s4].[TotalSingleSelectionQuestions], [s4].[TotalSources], [s4].[TotalTrueFalseQuestions], [s4].[Verified], [s4].[Version], [c].[Id], [c4].[Id], [s3].[ScannerId], [s3].[CategoryId], [s3].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c0].[Id], [c0].[ParentId], [c0].[Position]
FROM [Categories] AS [c0] WITH (NOLOCK)
WHERE [c0].[Active] = CAST(1 AS bit) AND [c0].[Deleted] = CAST(0 AS bit)
) AS [c4] ON [c].[Id] = [c4].[ParentId]
INNER JOIN (
SELECT [c2].[ScannerId], [c2].[CategoryId], [s].[Id]
FROM [CategoryScanners] AS [c2]
INNER JOIN [Scanners] AS [s] ON [c2].[ScannerId] = [s].[Id]
WHERE [s].[Active] = CAST(1 AS bit) AND [s].[Deleted] = CAST(0 AS bit)
) AS [s3] ON [c4].[Id] = [s3].[CategoryId]
INNER JOIN (
SELECT [s0].[Id], [s0].[Active], [s0].[Context], [s0].[ContextBackup], [s0].[ContextStorageMediaName], [s0].[ContextStorageMediaUrl], [s0].[Deleted], [s0].[FactErrors], [s0].[FactErrorsExplanation], [s0].[Facts], [s0].[FactsBackup], [s0].[FactsStorageMediaName], [s0].[FactsStorageMediaUrl], [s0].[Position], [s0].[ProcessorGenerateImagePrompt], [s0].[Prompt], [s0].[ScannerId], [s0].[SpellingErrors], [s0].[SpellingErrorsExplanation], [s0].[StorageMediaName], [s0].[StorageMediaUrl], [s0].[Summary], [s0].[SummaryBackup], [s0].[SummaryStorageMediaName], [s0].[SummaryStorageMediaUrl], [s0].[Title], [s0].[TitleSlug], [s0].[TotalFillTheBlankSelectionQuestions], [s0].[TotalMultipleSelectionQuestions], [s0].[TotalOrderingQuestions], [s0].[TotalQuestionPoints], [s0].[TotalQuestions], [s0].[TotalShortAnswerQuestions], [s0].[TotalSingleSelectionQuestions], [s0].[TotalSources], [s0].[TotalTrueFalseQuestions], [s0].[Verified], [s0].[Version]
FROM [ScannerCards] AS [s0]
WHERE [s0].[Active] = CAST(1 AS bit) AND [s0].[Deleted] = CAST(0 AS bit)
) AS [s4] ON [s3].[Id] = [s4].[ScannerId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [c4].[Position], [c4].[Id], [s3].[Id], [s3].[ScannerId], [s3].[CategoryId], [s4].[TitleSlug]
|
| 7. |
info: 2025-04-26 01:27:29.726 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
8ms [Parameters=[@__id_0='293fa425-4ae3-34b3-4b22-9d091fec9347', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [s5].[ScannerId], [s5].[CategoryId], [s5].[Id], [s5].[Active], [s5].[CheatSheet], [s5].[CheatSheet2], [s5].[Deleted], [s5].[FactErrors], [s5].[FactErrorsExplanation], [s5].[ParentCategory2Id], [s5].[ParentCategoryId], [s5].[ProcessorGenerateImagePrompt], [s5].[Prompt], [s5].[Reference], [s5].[ReferenceSlug], [s5].[SiteId], [s5].[SpellingErrors], [s5].[SpellingErrorsExplanation], [s5].[Summary], [s5].[Title], [s5].[TitleBackup], [s5].[TitleSlug], [s5].[TotalCards], [s5].[TotalCards2], [s5].[TotalCategories], [s5].[TotalPages], [s5].[Verified], [c].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c3].[ScannerId], [c3].[CategoryId], [s1].[Id], [s1].[Active], [s1].[CheatSheet], [s1].[CheatSheet2], [s1].[Deleted], [s1].[FactErrors], [s1].[FactErrorsExplanation], [s1].[ParentCategory2Id], [s1].[ParentCategoryId], [s1].[ProcessorGenerateImagePrompt], [s1].[Prompt], [s1].[Reference], [s1].[ReferenceSlug], [s1].[SiteId], [s1].[SpellingErrors], [s1].[SpellingErrorsExplanation], [s1].[Summary], [s1].[Title], [s1].[TitleBackup], [s1].[TitleSlug], [s1].[TotalCards], [s1].[TotalCards2], [s1].[TotalCategories], [s1].[TotalPages], [s1].[Verified]
FROM [CategoryScanners] AS [c3]
INNER JOIN [Scanners] AS [s1] ON [c3].[ScannerId] = [s1].[Id]
WHERE [s1].[Active] = CAST(1 AS bit) AND [s1].[Deleted] = CAST(0 AS bit)
) AS [s5] ON [c].[Id] = [s5].[CategoryId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [s5].[Id], [s5].[ScannerId], [s5].[CategoryId]
|
| 8. |
info: 2025-04-26 01:27:30.080 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
18ms [Parameters=[@__site_Id_0='63d6eb4e-8e39-4ac6-8f69-55ee76feccce', @__item_Left_1='2433', @__item_Right_2='2438'], CommandType='Text', CommandTimeout='30']
SELECT [c].[Id], [c].[Active], [c].[Deleted], [c].[Description], [c].[DescriptionBackup], [c].[Left], [c].[ParentId], [c].[Position], [c].[ProcessorGenerateImagePrompt], [c].[Right], [c].[SiteId], [c].[StorageMediaName], [c].[StorageMediaUrl], [c].[Title], [c].[TitleBackup], [c].[TitleSlug], [c].[TotalChildren], [c].[TotalScanners], [c].[TotalYoutubeVideos]
FROM [Categories] AS [c] WITH (NOLOCK)
WHERE [c].[SiteId] = @__site_Id_0 AND [c].[Left] <= @__item_Left_1 AND [c].[Right] >= @__item_Right_2 AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Left]
|
| 210 ms |
