A large turntable rotates about a fixed vertical axis, and has a moment of inert

Question

A large turntable rotates about a fixed vertical axis, and has a moment of inertia of 900 kgm^2. A child of g is initially standing at the center of the turntable, and the system rotates at a rate of 2.5 rad/sec. The child suddenly runs along the radius and stops at a point 2.0 meters from the center. What is the angular speed of the turntable when the child is at this location? What frictional force would be needed to hold the child at this spot? In class, we discussed how ice skaters, gymnasts, and high divers use conservation of angular momentum to make some of their moves. Explain in class terms how they use this conservation law.

Explanation / Answer

2.5 rad/sec = 23.873241491063457 RPM
23.873241491063457 RPM = 1 rotation in 2.5 sec
= 2/ T =2/ 2.5 = 2.51327 radian /s
Initial angular momentum = 900*2.513
Final angular momentum [900 + 40 *2^2] 2
Angular momentum is conserved.
[900 + 40 *2^2] 2 = 900 1
2 = 900 *2.51327 / [900 + 40 *2^2]
2 = 2.134 radian /s

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