A person of mass 76 kg stands at the center of a rotating merry-go-round platfor

Question

A person of mass 76 kg stands at the center of a rotating merry-go-round platform of radius 2.5 m and moment of inertia 880 kgm2 . The platform rotates without friction with angular velocity 0.95 rad/s . The person walks radically 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

A) Apply conservation of angular momentum

I2*w2 = I1*w1

(I_merry + I_person)*w2 = I_merry*w1

(880 + 75*2.5^2)*w1 = 880*0.95

==> w1 = 880*0.95/(880 + 75*2.5^2)

= 0.62 rad/s

B)

KEI = 0.5*I1*w1^2

= 0.5*880*0.95^2

= 397.1 J

KEf = 0.5*I2*w2^2

= 0.5*(880 + 75*2.5^2)*0.62^2

= 259.2 J

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