Three children each of mass 35kg are playing on a merry-go-round (MGR) of mass 6

Question

Three children each of mass 35kg are playing on a merry-go-round (MGR) of mass 61kg and radius 1.7m. Initially one child stands halfway out to the edge and the merry-go-round has angular velocity of 2.4 rad/s. a) What is the linear speed of the child? One of the other children jumps onto the edge of the MGR. b) What is the new angular velocity? Finally the third child pushes on the edge of the MGR with a force of 75N and slows it to a stop (the coefficient of friction is 0.26). c) What is the angular acceleration and how long does it take to stop?

Explanation / Answer

a)v=r=0.5*1.7*2.4=2.04m/s

b) I1=0.5MR^2+mr^2=0.5*61*1.7*1.7+35*1.7*1.7*0.5*0.5=113.43

1=2.4rad/s

I2=113.43+35*1.7*1.7=214.58

2=I11/I2=113.43*2.4/214.58=1.26rad/s

c)

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