Question

A person of mass 72 kg stands at the center of a rotating merry-go-round platform of radius 2.7 m and moment of inertia 860 kg?m2 . The platform rotates without friction 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.

Calculate the rotational kinetic energy of the system of platform plus person before and after the person's walk

Answer 1

Initial angular momentum Li = Imerry*w1

after the person walks to edge

final angular momentum Lf = (Imerry + m*r^2)*w2

from conservation of angular momentum

Lf = Li

(860 + (72*2.7^2))*w2 = 860*0.95

w2 = 0.59 rad/s

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rotation kinetic energy before person walk

Kbefore = (1/2)*Imerry*w1^2 = (1/2)*860*0.95^2 = 388 J

rotation kinetic energy before person walk to edge

Kafter = (1/2)*(Imerry + m*r^2)*w2^2

Kafter = (1/2)*(860 + (72*2.7^2))*0.59^2 = 241 J