Problem 8.61 A person of mass 71 kg stands at the center of a rotating merry-go-

Question

Problem 8.61 A person of mass 71 kg stands at the center of a rotating merry-go-round platform of radius 3.4 m and moment of inertia 950 kgm2 . The platform rotates without friction with angular velocity 1.8 rad/s . The person walks radially to the edge of the platform.

Part A Calculate the angular velocity when the person reaches the edge. Express your answer using two significant figures.

Part B 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

a)

Angular momentum P is constant. P = I*, where I = moment of inertia of the system. When the person is at the

center of the platform, there is no contribution to moment of inertia, so initial angular momentum is

P0 = I0*0

When the person moves to the edge of the platform, he adds his moment to the total, so

I1 = I0 + M*r²

P0 = P1, so I0*0 = (I0 + M*r²)*1

1 = 0*I0/(I0 + M*r²)

1 = 1.8*950/(950 + 71*3.4²) = 0.96 rad/s
b)

Kinetic energy = 0.5*I*²

KE before = 0.5*950*1.8² = 1539 J

KE after = 0.5*(950 + 71*3.4²)*(0.96²) = 815.96J

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