Exercise 10.45 Part A Find the angular speed of the turntable after the parachut

Question

Exercise 10.45 Part A Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.) A large wooden turntable in the shape of a flat uniform disk has a radius of 2.00 m and a total mass of 140 kg The turntable is initially rotating at 4.00 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 rad/s Submit My Answers Give Up Part B Compute the kinetic energy of the system before the parachutist lands. Submit My Answers Give Up Part C Compute the kinetic energy of the system after the parachutist lands

Explanation / Answer

moment of inertia of disk = I1 = 0.5*m1*r^2

initial angular momentum = Li = I1*w1

--------------------

moment of inertia of parachitist = I2 = m2*r^2

final angular momentum = Lf = (I1+I2)*w2

from momentum conservation

Lf = Li

((0.5*140*2^2)+(80*2^2))*w2 = 0.5*140*2^2*4

w2 = 1.87 rad/s

+++++

K1 = 0.5*I1*w1^2 = 0.5* 0.5*140*2^2*4^2 = 2240 J

++++++++++

K2 = 0.5*(I1+I2)*w2^2 = 0.5*((0.5*140*2^2)+(80*2^2))*1.87^2 = 1049.1 J

++++++

D)

here the momentu is conserved but not the energy

the table and parachutist couplelled inelastically

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