Question

A wheel is rotating at a rate of 2.0 rev every 3.0s. through what angle, in radian , does the wheel rotate in 1.0s?​

Answer 1

`4 \pi`

Step-by-step explanation:

First of all, let's convert 2.0 rev into radians:

`1.0 rev = 2\pi rad\\2.0 rev = 4 \pi rad`

This means that the angular speed of the wheel is

`\omega = 2.0 rev/s = 4 \pi rad/s`

The angle through which the wheel rotates in a time t is given by

`\theta=\omega t`

And substituting t=1.0 s, we find

`\theta=(4\pi rad/s)(1.0 s)=4 \pi rad`