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 140kg. The turntable is initially rotating at 3.00rad/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. Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.) w2=1.40 rad/s Correct Part B Compute the kinetic energy of the system before the parachutist lands. K1= J Incorrect; Try Again; 4 attempts remaining Part C Compute the kinetic energy of the system after the parachutist lands. K2= J

Explanation / Answer

A) initial moment of inertia Ii = MR^2 /2 = 140 x 2^2 /2 = 280 kg.m^2

initial angular velocity wi = 3 rad/s

Final moment of inertia If = MR^2 /2   + mr^2

   = 280 + 80x2^2 = 600 kg.m^2

Applying angular momentum (Iw) conservation,

Iiwi = Ifwf

280 x 3 = 600 x wf

wf = 1.4 rad/s

B) K = Iw^2 /2   = 280 x 3^2 /2 =1260 J

C) K = 600 x 1.4^2 /2 = 588 J

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