A person of mass 75 kg stands at the center of a rotating merry-go-round platfor

Question

A person of mass 75 kg stands at the center of a rotating merry-go-round platform of radius 3.1 m and moment of inertia 870 kg middot m^2 The platform rotates without function with angular velocity 0.95 rad/s. The person walks radially to the edge of the platform Calculate the angular velocity when the person reaches the edge. Express your answer using three significant figures and include the appropriate units. Calculate the rotational kinetic energy of the system of platform plus person before and after the person's walk. Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Explanation / Answer

I1w1 = I2w2
so Inertia 1 times angular velocity 1 equals Inertia 2 times angular velocity 2

When the person walks to the edge, they have a moment of inertia due to a point mass
I = mr2 = (75 kg)(3.1 m)^2 = 720.75 kgm2

the total moment of inertia after they walk to the edge is
I2 = 1500 kgm2 + 720.75 kgm2 = 2220.75 kgm2

I1w1 = I2w2
(1500 kgm2)(2.5 rad/s) = (2220.75kgm2)w2
w2 = 1.689 rad/s

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