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

$w_0 = 2\pi \frac{33.3}{60}$

$w_0 = 3.49 rad/s$

final angular speed is given by 78 rpm

$w_f = 2\pi \frac{78}{60}$

$w_f = 8.17 rad/s$

now by using kinematics we will have

$w_f = w_0 + \alpha * t$

$8.17 = 3.49 + 2.15 * t$

$t = 2.17 seconds$