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Kinetic Energy and Merry Go Round

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A merry-go-round of mass M=120kg and radius 5m rotates with an angular velocity ωo=3rad/s. A block of mass MA=90kg sits a distance RA=4m from the axis of rotation. At time t=0s, Bob (mB=70kg) jumps on the merry-go-round so that he lands a distance of RB=3m from the axis of rotation. Assume the merry-go-round has a moment of inertia given by: I=MR2/2.

a) What are the moments of inertia of the system before (just MA and merry-go-round) and after (MA, merry-go-round, and Bob) Bob jumps on?


b) What is the angular velocity of the system after Bob jumps on?


c) If Bob wants the merry go round to return to its original angular velocity, where should he place the mass MA, assuming he stays at RB?
new RA=_____________

d) Determine the Kinetic energy of the system before Bob jumps on (KEo), after Bob jumps on(KE'), and after Bob moves the mass in part c (KE'') KEo=_____________

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Solution Summary

The kinetic energy and Merry Go Rounds are examined.

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Motion of merry-go-round before and after person jumps onto it

A disk-shaped merry-go-round of radius 2.63 m and mass 155 kg rotates freely with an angular speed of .667 rev/s. A 59.4 kg person running tangential to the rim of the merry-go-round at 3.38 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim.

Calculate the initial and final kinetic energies of this system.

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