Question

A uniform disk turns at 3.1 rev/s around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk. They then turn together around the spindle with their centers superposed. (Figure 1)

Part A What is the angular frequency in rev/s of the combination?

Answer 1

The moment of inertia of the disk is

The moment of inertia of rod about its center is

Because it is given that the length of the rod is equal to the diameter of disk.

Here, conservation of angular momentum takes place, which states that

Initial angular momentum = final angular momentum