A student of mass m = 56 kg wants to measure the mass of a playground merry-go-r

Question

A student of mass m = 56 kg wants to measure the mass of a playground merry-go-round, which consists of a solid metal disk of radius R = 1.5 m that is mounted in a horizontal position on a low-friction axle. She tries an experiment: She runs with speed v = 7.5 m/s toward the outer rim of the merry-go-round and jumps on to the outer rim, as shown in the figure. The merry-go-round is initially at rest before the student jumps on and rotates at 1.3 rad/s immediately after she jumps on. You may assume that the student's mass is concentrated at a point.

(a) What is the mass of the merry-go-round?


(b) If it takes 36 s for the merry-go-round to come to a stop after the student has jumped on, what is the average torque due to friction in the axle?


(c) How many times does the merry-go-round rotate before it stops, assuming that the torque due to friction is constant?

Explanation / Answer

conservation of angular momentum
m r v = ( 1/2 M R^2 + m R^2) w

56*1.5*7.5 = (0.5*M*1.5^2+56*1.5^2)*1.3
M=318.77 kg

b) w = w0 + alpha t

0 = 1.3 + alpha*36
alpha = -0.036

torque = I alpha = 1/2*318.77*1.5^2*0.036=12.91 Nm

c)angle = w0 t + 1/2 a lpha t^2 =1.3*36 - 0.5*0.036*36^2=23.47 rad
3.7 times

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