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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?

Io=_____________
I'=_____________

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

ω'=_____________

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=_____________
KE'=_____________
KE''=_____________

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https://brainmass.com/physics/rotation/kinetic-energy-merry-go-round-364145

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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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