Answer to Question #267440 in Mechanics | Relativity for Ahanaf

Question

A wet socks clinging to the inside of a washing machine drum which is spinning at a speed of 4.7 m/s. The radius of the drum is 30 cm.

(a) As the drum slows down after the washing is done at an angular retardation of 3.25 rad/sec^2 Find the time taken and number of rotations before it stops.

Answer 1

Explanations & Calculations

• The initial angular velocity is

$\qquad\qquad \begin{aligned} \small \omega_0&=\small \frac{v}{r}=\frac{4.7}{0.3m}\\ &=\small 15.7\,rads^{-1} \end{aligned}$

• Since the retardation is constant, the 4 equations equivalent to the linear motion can be used as the way it is used in angular motion.
• Therefore, time will be,

$\qquad\qquad \begin{aligned} \small \omega_f&=\small \omega_0+\alpha t\\ \small t&=\small \frac{0-15.7}{-3.25}\\ &=\small 4.8\,s \end{aligned}$

• If the number of rotations is $\small n$, then the total length of rotation is $\small n\times2\pi=2n\pi$. Then,

$\qquad\qquad \begin{aligned} \small \omega_f^2&=\small \omega^2_0+2\alpha \theta\\ \small \theta&=\small \frac{0^2-15.7^2}{-2\times3.25}\\ \small 2n\pi&=\small 37.9\\ \small n&=\small 19\,\text{rotations} \end{aligned}$