Question

During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 31.7 rad/s. Find the angular displacement Δθ of the tub during a spin of 98.3 s, expressed both in radians and in revolutions.

Answer 1

`\Delta \theta = 3116.11\,rad` and
`\Delta \theta = 495.944\,rev`

Step-by-step explanation:

The tub rotates at constant speed and the kinematic formula to describe the change in angular displacement (
`\Delta \theta`), measured in radians, is:

`\Delta \theta = \omega \cdot \Delta t`

Where:

`\omega` - Steady angular speed, measured in radians per second.

`\Delta t` - Time, measured in seconds.

If
`\omega = 31.7\,(rad)/(s)` and
`\Delta t = 98.3\,s`, then:

`\Delta \theta = \left(31.7\,(rad)/(s) \right)\cdot (98.3\,s)`

`\Delta \theta = 3116.11\,rad`

The change in angular displacement, measured in revolutions, is given by the following expression:

`\Delta \theta = (3116.11\,rad)\cdot \left((1)/(2\pi) (rev)/(rad) \right)`

`\Delta \theta = 495.944\,rev`