A person of mass 75 kg stands at the center of a rotatingmerry-go-round platform

Question

A person of mass 75 kg stands at the center of a rotatingmerry-go-round platform of radius 3.1 m and moment of inertia 1400 kg·m2. The platformrotates without friction with angular velocity 2.0 rad/s. The person walks radially to the edgeof the platform.
(a) Calculate the angular velocity when the person reaches theedge. ____rad/s
(b)Calculate the rotational kinetic energy of the system of platformplus person before and after the person's walk. ____ J(before) ____ J(after)
(a) Calculate the angular velocity when the person reaches theedge. ____rad/s
(b)Calculate the rotational kinetic energy of the system of platformplus person before and after the person's walk. ____ J(before) ____ J(after)

Explanation / Answer

Given that
The mass of the person is m = 75 kg The radius of the merry-go-round is r = 3.1 m The moment of inertia is I1 = 1400kg.m2 The platform rotates without friction with angular velocity1 = 2.0
Since there is no external force on the system then the angularmomentum is conserved                               I1*1 = I2*2 where I2 = I1 + mr2 is thenew moment of inertia of the system Then 2 =I1*1 / I2               = ------------ rad/s The initial rotational kinetic energy is Ki =(1/2)I1*12                                                           = ---------------- J The final rotational kinetic energy is Kf =(1/2)I2*22                                                           = ---------------- J
Substitute values.
                              I1*1 = I2*2 where I2 = I1 + mr2 is thenew moment of inertia of the system Then 2 =I1*1 / I2               = ------------ rad/s The initial rotational kinetic energy is Ki =(1/2)I1*12                                                           = ---------------- J The final rotational kinetic energy is Kf =(1/2)I2*22                                                           = ---------------- J
Substitute values.
                                                          = ---------------- J
Substitute values.

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