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

Question

A large wooden turntable in the shape of a flat uniform disk has a radius of 2.00 m and a total mass of 130 kg. The turntable is initially rotating at 2.00 rad/s about a vertical axis through its center Suddenly, a 80.0-kg parachutist makes a soft landing on the turntable at a point near the outer edge. session Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.) omega_2 = __________ rad/s Compute the kinetic energy of the system before the parachutist lands. K_1 = _________ J Compute the kinetic energy of the system after the parachutist lands. K_2 = __________ J Why are these kinetic energies not equal? Essay answers are limited to about 500 words (3800 characters maximum. including spaces).

Explanation / Answer

A) I before = 1/2*M*R^2 = 1/2*130*2.0^2 = 260kg-m^2

I after, I = 260 + 80*2.0^2 = 580 kg-m^2

So I *)before = I*)after

So after = 260*2.00 rad/s/580 = 0.896 rad/s

B) K before = 1/2*I*^2 = 1/2*260*2^2 = 520J

C) K after = 1/2*I*^2 = 1/2*580*0.896^2 = 259.84J

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