Question

# A 47.0-kg girl sits on a 330-kg playground "merry-go-round" (large rotating disk). Initally she sits at...

A 47.0-kg girl sits on a 330-kg playground "merry-go-round" (large rotating disk). Initally she sits at a radium of 1.00m from the center and it spins at a rate of one turn in 2.60 s. Consider what happens when she carefully moves to the outside edge of the merry-go-round.

If the radius of the disk is 3.50 m, compute its angular speed once the girl has made it all the way to the rim. 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)

Initial angular velocity = i = 2?/2.60 rad/sec

Here using conservation of angular momentum

I11 = I22 , Here I is moment of inertia.

I1 = (1/2)MdiskR2 = 2021.25kg.m2

I2 = I1 + mboyR2 = 2021.25 + 47×3.52 = 2597 kg.m2

2021.25×2?/(2.6) = 2597×2

2 = 1.8806 rad/sec

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