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?

2.17 s

Explanation:

Here, w0 = 33.3 rpm = 33.3 / 60 rps

= 2 * pi * 33.3 / 60 rad / s

= 3.4854 rad / s

w = 78 rpm = 78 / 60 rps

= 2 * pi * 78 / 60 = 8.164 rad / s

a = 2.15 rad/s^2

Use first equation of motion for rotational motion

w = w0 + a t

8.164 - 3.485 = 2.15 * t

t = 2.17 s