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 100 kg . The turntable is initially rotating at 2.00 rad/s about a vertical axis through its center. Suddenly, a 60.0-kg parachutist makes a soft landing on the turntable at a point near the outer edge.

a.Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.)

b.Compute the kinetic energy of the system before the parachutist lands.

c.Compute the kinetic energy of the system after the parachutist lands.

d.Why are these kinetic energies not equal?

Explanation / Answer

Ans: The radius of the disk r=2m

The mass of disk M=100kg

So, The moment of inertia of the disk =I=mr2=400kgm2

The angular velocity of the disk is w=2rad/s

The kinetic energy of the disk before parachutist land=K1=.5*I*w2=800J

  The mass of the parachutist m=60kg

The kinetic energy of the parachutist is .5*m*r2*w2=480J

So, The kinetic energy of the system after parachutist lands is K2=800-480=320J=.5*(m+M)*r2*W2

Thus, W=Angular speed of the system after parachutist lands =320*2/(160*4)=1rad/s

The kinetic energy of the system decreased because of increase in mass of the system

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