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

Answer:

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

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 $\omega = 31.7\,\frac{rad}{s}$ and $\Delta t = 98.3\,s$, then:

$\Delta \theta = \left(31.7\,\frac{rad}{s} \right)\cdot (98.3\,s)$

$\Delta \theta = 3116.11\,rad$

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

$\Delta \theta = (3116.11\,rad)\cdot \left(\frac{1}{2\pi} \frac{rev}{rad} \right)$

$\Delta \theta = 495.944\,rev$