Question

A uniform disk with a mass of 900 g and radius 17.0 cm is rotating on frictionless bearings with an rotational speed of 18.0 Hz when Jill drops a 180-g clod of clay on a point 8.70 cm from the center of the disk, where it sticks. What is the new rotational speed of the disk?

Answer 1

According to the law of conservation of the angular momentum
I•ω1 = (I +Io) • ω2
M•R^2/2 • 2•π•n1 = (M•R^2/2 + mr^2) • 2•π•n2
n2= (M•R^2/2 • n1)/ (M•R^2/2 + mr^2) (Hz)
where M =0.9 kg, R=0.17 m, n1=18 Hz,
m =0.18 kg, r =0.087 m