A 1.6 kg disk with radius 0.63 m is rotating freely at 55 rad/s around an axis perpendicular to its center. A second disk that is not rotating is dropped onto the first disk so that their centers align, and they stick together. The mass of the second disk is 0.45 kg and its radius is 0.38 m. What is the angular velocity of the two disks combined?

Question

drwls · Answer

Compute the moment of inertia of each disc using the formula

I = (1/2) M R^2

For example, for the initially rotating disc,
I1 = (1/2)(1.6)(0.63)^2 = 0.318 kg m^2
I2 = (1/2)(0.46)(0.38)^2 = ____?

Then apply the law of conservation of angular momentum in this form:

I1*w1 = (I1 + I2) w2

and solve for w2.