Suppose a child of mass 55 kg is on the outer edge of a merry-go-round with a mo

Question

Suppose a child of mass 55 kg is on the outer edge of a merry-go-round with a moment of inertia of 510 kg-m2 and with a radius of 3.50 m. At time t-O, the child and the merry-go-round rotate at an angular velocity of 3.05 rad/s, when the child decides it would be fun to try to walk to the center. Ignore friction in the bearing. 4. a. Find the final angular velocity, assuming the child succeeds in making it to the center Mc 55 2 b. Find the amount of work the child has to provide to get to the center.

Explanation / Answer

(a)

initial angular momentu Li = (Imerry + m*R^2)*wi

final angular momentum Lf = (Imerry)*wf

m = mass of child = 55 kg

R = radius of merry go = 3.5 m

wi = initial angular speed = 3.05 rad/s

from conservation of angular momentum

Lf = Li

(510 + (55*3.5^2))*3.05 = 510*wf

final angular velocity wf = 7.08 rad/s

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(b)

amount of work done W = (1/2)*I*(wf^2 - wi^2)

Work = (1/2)*510*(7.08^2-3.05^2)

work = 10410.1 J

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