AP Physics B : Understanding Linear-Rotational Equivalents

Study concepts, example questions & explanations for AP Physics B

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Example Questions

Example Question #1 : Other Circular And Rotational Motion Concepts

A wheel of radius \displaystyle r rolls along a flat floor and makes \displaystyle n rotations over a period of time. What distance \displaystyle d has the wheel traveled?

Possible Answers:

\displaystyle n\pi r

\displaystyle \frac{\pi r}{n}

\displaystyle n\pi r^2

\displaystyle \frac{2\pi r}{n}

\displaystyle n(2\pi r)

Correct answer:

\displaystyle n(2\pi r)

Explanation:

In order to find the distance the wheel travels, we need a way to convert angular displacement to linear displacement. We know that the circumference of a circle (or a wheel, in this case) is \displaystyle 2\pi r. This means that in one rotation, the wheel would travel a distance equal to its circumference.

Distance of one rotation equals: \displaystyle 2\pi r.

Since the wheel travels \displaystyle n rotations, the total distance that the wheel travels will be equal to the distance traveled by one rotation multiplied by the number of rotations.

Distance of \displaystyle n rotations equals: \displaystyle n(2\pi r)

\displaystyle d=n(2\pi r)

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