Question

A lazy Susan consists of a heavy plastic disk mounted on a frictionless bearing resting on a vertical shaft through its center. The cylinder has a radius R = 10 cm and mass M = 0.24 kg. A cockroach (mass m = 0.015 kg) is on the lazy Susan, at a distance of 10 cm from the center. Both the cockroach and the lazy Susan are initially at rest. The cock&roach then walks along a circular path concentric with the axis of the lazy Susan at a constant distance of 10 cm from the axis of the shaft. If the speed of the cockroach with respect to the lazy Susan is 0.01 m/s, what is the speed of the cockroach with respect to the room?

Answer 1

Assume the total angular momentum remains zero (due to frictionless bearing). If the angular velocity of the lazy susan is w, its angular momentum is I*w, where I = (1/2)M*R^2

The angular momentum of the kokroach is equal and opposite to that of the lazy susan.

I*w = m*R*v
where v is the speed of the kokroach with respect to the room, m is the roach mass, and R = 0.10 m.
You also need to use the equation
v - R*w = 0.01 m/s
for the relative velocity

Solve for v.

Answer 2

.04