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AP Physics B : Understanding Linear-Rotational Equivalents

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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:

$n\pi r$ $\displaystyle n\pi r$

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

$n\pi r^2$ $\displaystyle n\pi r^2$

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

$n(2\pi r)$ $\displaystyle n(2\pi r)$

Correct answer:

$n(2\pi r)$ $\displaystyle n(2\pi r)$

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 $2\pi r$ $\displaystyle 2\pi r$ . This means that in one rotation, the wheel would travel a distance equal to its circumference.

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

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: $n(2\pi r)$ $\displaystyle n(2\pi r)$

$d=n(2\pi r)$ $\displaystyle d=n(2\pi r)$

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AP Physics B : Understanding Linear-Rotational Equivalents

Study concepts, example questions & explanations for AP Physics B

All AP Physics B Resources

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Example Question #1 : Other Circular And Rotational Motion Concepts

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