physics
posted by marcel .
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?

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. 
.04