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=(\omega-\omega_0)/(t)`

Using the formula

`-3.73=(0-18.9)/(t)`

`t=(-18.9)/(-3.73)=5.067 s`

b.
`\theta=\omega_0t+(1)/(2)\alpha t^2`

Using the formula

`\theta=18.9(5.067)+(1)/(2)(-3.73)(5.067)^2`

`\theta=47.88 rad`

`\theta=2743.3 degree`