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

I₁₁ = I₂₂ , Here I is moment of inertia.

I₁ = (1/2)M_diskR² = 2021.25kg.m²

I₂ = I₁ + m_boyR² = 2021.25 + 47×3.5² = 2597 kg.m²

2021.25×2?/(2.6) = 2597×₂

₂ = 1.8806 rad/sec