Question

The turntable reaches an angular speed of 45 rev/min in 4.10 s after being turned on. What is its angular acceleration?

Answer 1

You are given your initial and final velocities, as well as your time value, so you should be able to solve it with a simple acceleration formula. However, the catch is that your time is in seconds and your velocity in minutes. I would suggest doing 4.1/60 to get seconds into minutes, and then doing 45 divided by that number. Hope that helped.

Answer 2

The "angular kinematics" are exactly like their linear counterparts. So if you would normally find the linear acceleration using

\[a = \frac{ \Delta v}{\Delta t}\]

then similarly, you would find the angular acceleration

\[ \alpha = \frac{\Delta \omega}{\Delta t}\]

Then like @Potatocracy said, be sure to convert your angular velocity from rev/min to rev/sec

\[ \omega = \Big( \frac{4.5 \ rev}{ min} \Big) \Big( \frac{1 \ min}{60 \ s } \Big)= \frac{4.5 \ rev}{ 60 s}\]