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 2.05 m and a total mass of 130 kg. The turntable is initially rotating at 3.40 rad/s about a vertical axis through its center. Suddenly, a 72.5-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.

Explanation / Answer

I1 = ½Mt*R² = 0.5 x 130 x 2.052= 273.1625 kgm²

I2 = I1+Mp*R² = 273.1625+ 72.5*2.05² = 577.84 kgm²

w2 = [I1/I2]*w1 = [273.162/577.84]*3 = 1.63 rad/sec

K before = 1/2*I*^2 = 1/2*273.16*3.4^2 = 1578J

K after = 1/2*I*^2 = 1/2*577.84*1.63^2 = 768J

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