A large wooden turntable in the shape of a flat disk has a radius of 2.0 m and a

Question

A large wooden turntable in the shape of a flat disk has a radius of 2.0 m and a total mass of 120 kg.The turntable is initially rotating about a vertical axis through its center with an angular velocity of 3.0 rad/s. A 100 kg bag of sand is dropped vertically from a very small height onto the turntable at a point near the outer edge.
A) Find the angular velocity of the turntable after the bag is dropped.(assume the bag of sand can be treated as a particle).
B) Compute the kinetic energy of the system before and after the bag is dropped.Why are these kinetic energies not equal.

Explanation / Answer

A) Conservation of angular momentum
120*4*3 = (120*4+100*4)*x
=> x = 1.64 rad/sec
B) Before, 1/2Iw^2 = 2160 J
After, w^2/2(I1+I2) = 1183.424 J
These are not equal because some energy is lost as friction.

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