Question

How long does it take a wheel that is rotating at 33.3 rpm to speed up to 78.0 rpm if it has an angular acceleration of 2.15 rad/ s 2?

Answer 1

initial angular speed is given by 33.3 rpm

`w_0 = 2\pi (33.3)/(60)`

`w_0 = 3.49 rad/s`

final angular speed is given by 78 rpm

`w_f = 2\pi (78)/(60)`

`w_f = 8.17 rad/s`

now by using kinematics we will have

`w_f = w_0 + \alpha * t`

`8.17 = 3.49 + 2.15 * t`

`t = 2.17 seconds`