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 110 kg . The turntable is initially rotating at 4.00 rad/s about a vertical axis through its center. Suddenly, a 75.0-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

a)

let the final angular speed is wf

Using conservation of angular momentum

Ii * wi = If * wf

0.5 * 110 * 2^2 * 4 = ( 0.5 * 110 * 2^2 + 75 * 2^2) * wf

wf = 1.69 rad/s

the final angular speed is 1.69 rad/s

b)

for the kinetic energy before the landing ,

kinetic energy = 0.5 * 0.5 * 110 * 2^2 * 4^2

kinetic energy = 1760 J

c) for the kinetic energ after the landing

kinetic energy = 0.5 * ( 0.5 * 110 * 2^2 + 75 * 2^2) * 1.69^2

kinetic energy = 742.6 J

d)

kinetic energy is lost due to collision, heat and sound is produced

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