A large wooden turntable in the shape of a flat uniform disk has a radius of 2.3

Question

A large wooden turntable in the shape of a flat uniform disk has a radius of 2.30 m and total mass of 110 kg. The turntable is initially rotating at 3.20 rad/s about a vertical axis through its center. Suddenly, a 70.5-kg parachutist makes a soft landing on the turntable at a point near the outer edge. Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.) rad/s Compute the kinetic energy of the system before and after the parachutist lands. KE_before= ] KE_after= ] Why are these kinetic energies not equal

Explanation / Answer

moment of inertia of the disc, I1 = mr^2/2 = 110*2.30^2/2 = 291 kg-m^2

final momnet of inertia = 291 + (70.5*2.3^2) = 664 kg-m^2

from the law of conservation of angular momentum

I1w1 = I2w2

291*3.20 = 664 * w2

w2 = 1.40 rad/s

B)

KE before = 0.5Iw^2 = 0.5*291*3.2^2 = 1490 J

KE after = 0.5I2w2^2 = 0.5*664*1.4^2 = 650.72 J

kinetic energies are not equal becuase it is an inelastic collision

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