Four people are on a merry-go-round. All individuals are approximately 90 kg (20

Question

Four people are on a merry-go-round. All individuals are approximately 90 kg (200 lb). The merry-go-round has a radius of 2.4 m and a moment of inertia of 2100 kg m^2. The four people push on the merry-go-round equally and run around at 15 mph and then hop on the edge.

a) Find the new moment of inertia of the system once the four people jump on.

b) Three of the people quickly move to the center of the merry-go-round and in effect, taking themselves out of the system. The last person is still at the outer edge. What is the new rotational speed of the merry-go-round?

c) If the person at the edge can't hang on, at what tangential velocity will he fly off (in mph)?

Explanation / Answer

a) Inew = I + 4 x mr2

            = 2100 + 4 x 90 x2.42   = 4173.6 kg-m2

b) conserving angular moemntum,

v = 15mph = 6.7 m/s

= v/r = 6.7 / 2.4 = 2.79 rad/s

2100 x 2.79 + 4 x 90 x 6.7 x 2.4 = (2100 + 90 x 2.42 ) x

= 4.45 rad/s

c) vt = r = 4.45 x 2.4 = 10.68 m/s

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