Chapter 9, Problem 17SP

A wheel spins around exactly 6 times. How many radians does that correspond to?

To determine

The number of radians corresponding to the spinning of a wheel 6 times.

Answer to Problem 17SP

Solution: $12\pi$ radians.

Explanation of Solution

Given data:

The number of times the wheel spins is 6.

Formula used:

Since number of radians covered in one rotation is $2\pi$, Thus, the number of radians covered in n number of rotations is,

$\theta =2\pi n$

Explanation:

Consider the expression for number of radians covered during the spinning of a wheel

$\theta =2\pi n$

Here, $n$ is the number of times the wheel spins and $\theta$ is the number of radians covered by the wheel corresponding to $n$ spins.

Understand that the wheel spins 6 times. Therefore, substitute 6 for $n$

$\begin{array}{c}\theta =2\pi \left(6\right)\\ =12\pi \text{ radians}\end{array}$

Conclusion:

The spinning of the wheel 6 times corresponds to $12\pi$ radians.