The world\'s heaviest rabbit, Darius, is sitting on the edge of a merry-go-round

Question

The world's heaviest rabbit, Darius, is sitting on the edge of a merry-go-round. His mass is 22.2 kg, and the merry-go-round is a 150 kg iron disk with a radius of 2.5 m; it turns on perfectly frictionless bearings. The merry-go-round is at rest until Darius starts running in circles around its circumference. The giant bunny's speed relative to the ground is 5.0 m/s.

(a) What is the angular speed of the merry-go-round?

(b) At what speed is Darius running with respect to the part of the merry-go-round just below him?

Explanation / Answer

mass of rabbit = 22.2 kg

Moment of interia of rabbit about center = mr2 = 22.2*2.52 = 138.75 kg-m2

mass of merry-go-round = 150 kg

moment of inertia of merry-go-round(disc) = Mr2/2 = 150*2.52/2 = 468.75 Kg-m2

rabbits velocity relative to ground = 5 m/s

rabbits angular velocity relation to ground = v/r = 5/2.5 = 2 rad/s

By conservation of angular momentum

Initial angluar momentum = final angular momentum

=> 0 = 138.75*2 + 468.75*w

=> w = - 0.592 rad/s with respect to ground

a) angular speed of the merry-go-round = 0.592 rad/s with respect to ground in direction opposite to bunny

b) angular speed of darius with respect to the merry go round just below him = 2 + 0.592 = 2.592 radian/s

speed of Darius running with respect to the part of the merry-go-round just below him = angular speed * radius = 2.592*2.5 = 6.48 m/s

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