Question

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)

Wf=? rad/s

Answer #1

Initial angular velocity =
_{i}
= 2?/2.60 rad/sec

Here using conservation of angular momentum

I_{1}_{1}
= I_{2}_{2}
, Here I is moment of inertia.

I_{1} = (1/2)M_{disk}R^{2} =
2021.25kg.m^{2}

I_{2} = I_{1} + m_{boy}R^{2} =
2021.25 + 47×3.5^{2} = 2597 kg.m^{2}

2021.25×2?/(2.6) = 2597×_{2}

_{2}
= 1.8806 rad/sec

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