A 47-kg girl sits near the rim of a 330-kg playground \"merry-go-round\" (large

Question

A 47-kg girl sits near the rim of a 330-kg playground "merry-go-round" (large rotating disk) that spins at a rate of one turn in 2.2 s. Consider what happens when she carefully moves to the center of the disk. If the radius of the disk is 1.5 m, compute its angular speed once the girl has made it all the way to the center. Approximate the "merry-go-round" as an ideal uniform disk, and treat the girl as a "point mass" (a good approximation as long as her diameter is much smaller than that of the disk!)

Explanation / Answer

Moment of inertia of merry go round = 0.5 mr^2

I = 0.5 * 440 * 1.5^2

I = 495 kgm^2

from conseervation of angular momentun

I + mr^2) W1 = 0.5 mr^2 W

495 + (47* 1.5^2) *(1/2.2) = 0.5 * 330 * 1.5^2 * W

W = 1.462 rad/s

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