Question

A drum rotates around its central axis at an angular velocity of 18.9 rad/s. If the drum then slows at a constant rate of 3.73 rad/s2, (a) how much time does it take and (b) through what angle does it rotate in coming to rest?

Answer 1

Answer with Explanation:

We are given that

Initial angular velocity,$\omega_0=18.9 rad/s$

Angular acceleration,$\alpha=-3.73 rad/s^2$

a.We have to find the time taken by drum in coming to rest.

$\omega=0$

We know that

$\alpha=\frac{\omega-\omega_0}{t}$

Using the formula

$-3.73=\frac{0-18.9}{t}$

$t=\frac{-18.9}{-3.73}=5.067 s$

b.$\theta=\omega_0t+\frac{1}{2}\alpha t^2$

Using the formula

$\theta=18.9(5.067)+\frac{1}{2}(-3.73)(5.067)^2$

$\theta=47.88 rad$

$\theta=2743.3 degree$