Question

A drum rotates around its central axis at an angular velocity of 19.8 rad/s. If the drum then slows at a constant rate of 3.02 rad/s2, (a) how much time does it take and (b) through what angle does it rotate in coming to rest

Answer 1

a) Time taken =6.39 s

b) Angle of rotation while coming to rest = 188.17 rad

Explanation:

Initial angular velocity of the drum $\omega_{0} = 19.8 rad/s^{2}$

Angular acceleration of the drum $\alpha = -3.02 rad/s^{2}$

a.) We know that

$\omega =\omega_{0} + \alpha t$

$0 = 19.8 - 3.02 t$

$t = \frac{19.8}{3.02}$

$t = 6.39s$

b.) we know that

$\theta = \omega_{0} t + \frac{1}{2} \alpha t^{2}$

$\theta = 19.8 \times 6.39 + \frac{1}{2} \times 3.02 \times 6.39^{2}$

$\theta =188.17 rad$