# A drum rotates around its central axis at an angular velocity of 14.4 rad/s. If the drum then slows at a constant rate of 8.02 rad/s^2, (a) how much time does it take and (b) through what angle does it rotate in coming to rest?

Dec 3, 2015

$\left(a\right)$

$1.8 \text{s}$

$\left(b\right)$

$12.92$$\text{ rad}$

#### Explanation:

I will use the equations of motion:

(a)

$v = u + a t$

$\therefore 0 = 14.4 - 8.02 t$

$\therefore t = \frac{14.4}{8.02} = 1.8 \text{s}$

(b)

The angle through which it rotates is analogous to distance so we can use:

$s = u t + \frac{1}{2} a {t}^{2}$

$\therefore s = 14.4 \times 1.8 - \frac{1}{2} \times 8.02 \times {1.8}^{2}$

$s = 12.92$ $\text{rad}$