Question

A solid disk and a hoop are mounted on low friction bearings on the same axis and can be brought together so they couple and rotate as one unit. The disk with rotational inertia 2.8 kg*m*m about it central axis, is set spinning CCW at 420 rev/min. the hoop with rotational inertia 6.3 kg*m*m about its central axis, is set spinning clockwise at 610 rev/min. They then couple together. What is their angular speed after they couple?

Answer 1

We will have the following:

First, we transform the revolutions per second to radians, that is:

$\begin{cases}-420rev/\min =-840\pi/\min =-14\pi/s \\ \\ 610\text{rev}/\min =1220\pi/\min =\frac{61\pi}{3}/s\end{cases}$

Now, we will have that the final angular velocit will be given by:

$-14\pi/s+\frac{6\pi}{3}/s=-12\pi/s$

So, the angular speed after coupling is -12pi/s. [That is the total angular speed will be counterclock wise]