Question

a ring rotates ar 30rad/s and has a radius of 3m and a mass 0f 100kg. If a disk(mass=40kg and with a radius of 4m) is dropped on the ring so the centers are aligned, what will be the resulting rotational speed of the ring-disc combination?

Answer 1

Calculate the moments of inertia of the ring (I1 = M R^2) and the disc, (I2 = (/2)M R^2). Note that the M's and R's are different for each.

The angular momentum conservation equation takes the form
I1*w = (I1 + I2) w'

w' is the final angular velocity you want.

w' = [I1/(I1 + I2)] w
where w = 30 rad/s.