Elinor (25 kg) is playing on the (100kg, 2.5 meters wide) merry-go-round, but wa

Question

Elinor (25 kg) is playing on the (100kg, 2.5 meters wide) merry-go-round, but wants to go faster. Elinor stands in the middle, and Edward (35kg) pushes the merry-go-round from rest until the outside edge is moving 3.0 m/s, and then lets go.

a) What is the moment of inertia of the merry-go-round with Elinor at the center, and when she walks to the outside edge?

b) After it is up to speed, Elinor walks from the middle to the outside edge. What is the speed of Elinor once she reaches the outside edge of the merry-go-round?

Explanation / Answer

a) initial = Mr^2/2 = 100^1.25*1.25/2 + 24*1.25*1.25/4 = 207.017 kg-m^2

Final = 100^1.25*1.25/2 + 24*1.25*1.25 = 235.1423 Kg-m^2

b) I_1*w_1 = I_2*w_2

=> w_2 = 207.017*(3/1.25)/(235.1423) = 2.1129

=> V = w_2*R = 2.1129*1.25 = 2.64 m/s

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