Angular Velocity?

Question

A woman of mass m stands at the edge of a solid cylindrical platform of mass M and radius R. At t=0, the platform is rotating with negligible friction at angular velocity ωo about a vertical axis through its center, and the person begins walking with speed v (relative to the platform) toward the center of the platform.

a. Determine the angular velocity of the system, as a function of time.
b.What will be the angular velocity when the woman reaches the center?

Answer 1

This is solved by setting up conservation of angular momentum.

The moment of inertia of the system changes as she moves on the platform, but since she is moving radially, there is no additional angular acceleration due to her motion.

Io*ωo=I(t)*ω(t)
Io=.5*M*R^2+m*R^2
I(t)=.5*M*R^2+m*(R-v*t)^2

so
ω(t)=(.5*M*R^2+m*R^2)*ωo/
(.5*M*R^2+m*(R-v*t)^2)

When the woman reaches the center, the I of the system will be .5*M*R^2
so
ω(woman at center)=
(.5*M*R^2+m*R^2)*ωo/
(.5*M*R^2

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