A child of mass 30kg running at 3 m/s jumps onto the rimof a playground merry-go

Question

A child of mass 30kg running at 3 m/s jumps onto the rimof a playground merry-go-round of radius 1.5 meters and mass 150kg. Assume the merry-go-round is a disk. It it was initally atrest, what is its final angualr velocity? (neglect friction) Answer: 0.57 rad/s A child of mass 30kg running at 3 m/s jumps onto the rimof a playground merry-go-round of radius 1.5 meters and mass 150kg. Assume the merry-go-round is a disk. It it was initally atrest, what is its final angualr velocity? (neglect friction) Answer: 0.57 rad/s

Explanation / Answer

Angular momentum must be conserved. . Initial angular momentum = mass * speed * r = 30 * 3 * 1.5 =   135 . Final angular momentum =   total moment ofinertia * angular velocity = I . You have to find . .    I = moment of inertia ofmerry-go-round + moment of inertia of child = .           = (1/2) M r2   +   mr2 = (1/2) * 150 *1.502   +   30 *1.502   =    236.25 . Now finally... .     initial angular momentum =   final angular momentum .          135   =     236.25 * .    =   0.5714  rad/s    is the final angular velocity

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