Question

During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 33.3 rad/s. Find the angular displacement of the tub during a spin of 77.5 s, expressed both in radians and in revolutions.

Answer 1

The angular displacement of the tub will be 2580.75 rad or 411 revolutions.

Step-by-step explanation:

We know the relation between angular velocity (
`\omega`), the angular displacement (
`\theta`) and time (
`t`) is given by

`\omega = (\theta)/(t)`

Given
`\omega` =
`rad~s^(-1)` and the time (
`t`) required to complete a spin is 77.5 s.

Therefore, the required angular displacment (
`\theta`) is

`&& \theta = \omega * t\\&or,& \theta = 33.3~rad~s^(-1) * 77.5~s = 2580.75~rad`

Also we know that,

`&& 2 \pi~rad = 1~revolution\\&or,& 580.75~rad = (2580.75)/(2~\pi) \approx 411~revolutions`

So, the angular displacement of the tub will be 2580.75 rad or 411 revolutions.