A large wooden turntable in the shape of a flat uniform disk has a radius of 1.5

Question

A large wooden turntable in the shape of a flat uniform disk has a radius of 1.55 m and a total mass of 115 kg. The turntable is initially rotating at 3.25 rad/s about a vertical axis through its center. Suddenly, a 68.5-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.) rad/s (b) Compute the kinetic energy of the system before and after the parachutist lands. KEbefore KEafter- Why are these kinetic energies not equal?

Explanation / Answer

M =115 kg , r =1.55 m , m =68.5 kg, w1 = 3.25 rad/s

Moment of inertia of uniform disk = (1/2)Mr^2

(a) form conservation of angular momentum

I1w1 = I2w2

(0.5*115*1.55*1.55)*3.25 = (0.5*115 + 68.5)*1.55*1.55*w2

w2 =1.483 rad/s

(b) KEbefore = (1/2)I1w1^2

= 0.5*(0.5*115*1.55*1.55)*3.25*3.25 =729.57 J

K.Eafer = (1/2)I2w2^2

= 0.5*(0.5*115+68.5)*1.55*1.55*1.483*1.483 = 332.88 J

(c) after parachutist lands, angular velocity is changed. the landing is inelastic landing. So the final kinetic energy is not equal to initial kinetic enenrgy

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