A 81.5kg cadet stands at the edge of a stationary merry-go-round at rest (assume

Question

A 81.5kg cadet stands at the edge of a stationary merry-go-round at rest (assume the disk to be uniform cylindrical disk of radius 2.06m and mass of 145kg, where I= 1/2MR^2). The merry-go-round is mounted on frictionless axle. The cadet throws a shot-put of mass Ms=7.27kg with speed of 18.5m/s relative to the ground and tangent to the edge of the merry-go-round. A). Calculate the moment of inertia of the merr-go-round/cadet system after the shot-put is thrown (without the shot-put) relative to the center of the merry-go-round. treat cadet as point of mass. B). What is the initial angular momentum of the merry-go-round/cadet/shot-put combination before the shot-put was thrown? C). Calculate the angular momentum of the shot-put at the moment it leaves the merry-go-round/cadet system relative to the center of the merry-go-round. D). Calculate the angular momentum of the merry go round/cadet system at the moment that the shot-put leaves the system. E). Determine the velocity of the cadet immediately after the shot-put is thrown. Assume the cadet is on the edge and doesnt slide on the surface.

Explanation / Answer

(a) According to conservation of angular momentum we have

Li = Lf

Ii wi = If wf

(Ic + Imgr + Is ) wi = (Ic + Imgr) wf

A) The final moment of inertial after the shot put is thrown is

If = (Ic + Imgr) = ( 0 + Imgr ) = 0.5 M R2 = 0.5 * 145 * 2.06 * 2.06 = 307.667  kg m2

B) The initial angular momentum of the system is zero. As the marry-go-round is at rest.

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