college physics
posted by Anonymous on .
Suppose a 69 kg person stands at the edge of a 7.8 m diameter merrygoround turntable that is mounted on frictionless bearings and has a moment of inertia of 1600 kg*m^2. The turntable is at rest initially, but when the person begins running at a speed of 3.7 m/s (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable. Please help with stepbystep explanation.

The total angular momentum remains zero because of the frictionless bearings. The person and the turntable rotate about the axis of rotation in opposite directions.
Let w be the angular velocity of the turntable after "the person" begins running. His (or her) angular momentum about the axis is
M V R = M (3.7  R w) *R
Note that we have to use the speed V with respect to land, not the turntable. That is why R w has to be subtracted from the velocity with respect to the turntable.
Solve this equation for the angular velocity w:
I w = M (3.7  R w) *R
I w (1 + MR^2)= 3.7 M R