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Ch. 10 - Rotational Motion
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Giancoli Douglas 5th editionCh. 10 - Rotational Motion문제 10.6
10장, 문제 10.6

(II) A child rolls a ball on a level floor 3.1 m to another child. If the ball makes 12.0 revolutions, what is its diameter?

검증된 단계별 안내
1
Calculate the circumference of the ball using the formula for the circumference of a circle, which is \(C = 2\pi r\), where \(r\) is the radius of the ball. Since the diameter \(d = 2r\), the formula can also be written as \(C = \pi d\).
Determine the total distance the ball travels using the number of revolutions and the circumference. The total distance \(D\) traveled by the ball is the product of the number of revolutions and the circumference, \(D = \text{number of revolutions} \times C\).
Set up the equation using the given total distance traveled by the ball (3.1 m) and the expression for \(D\) from step 2. Substitute \(D = 3.1 \text{ m}\) and solve for the diameter \(d\).
Rearrange the equation to isolate \(d\) on one side. This can be done by dividing both sides of the equation by \(\pi\) and the number of revolutions.
Simplify the equation to find the expression for the diameter \(d\) of the ball.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m
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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Circumference of a Circle

The circumference of a circle is the distance around it, calculated using the formula C = πd, where d is the diameter. In this problem, knowing the circumference is essential to relate the number of revolutions the ball makes to the distance it travels.
추천 영상:
가이드 코스
05:08
Circumference, Period, and Frequency in UCM

Revolutions and Distance

One complete revolution of a circular object corresponds to a distance equal to its circumference. Therefore, if a ball makes multiple revolutions, the total distance traveled can be found by multiplying the number of revolutions by the circumference. This relationship is crucial for determining the diameter from the given distance.
추천 영상:
가이드 코스
05:58
Displacement in Multiple Revolutions

Unit Conversion

In physics problems, it is often necessary to ensure that all measurements are in compatible units. In this case, the distance traveled by the ball (3.1 m) and the diameter must be expressed in the same unit system, typically meters, to accurately calculate the diameter based on the revolutions made.
추천 영상:
가이드 코스
07:46
Unit Conversions
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