Question

A carousel has a radius of 1.70 m and a moment of inertia of 126 kg · m2 . A girl of mass 48.5 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.00 rad/s. Now the girl walks toward the center of the carousel and stops at a certain distance from the center d. The angular speed of the carousel is now 5.0 rad/s. How far from the center did the girl stop?

Answer 1

The girl stopped 23.4 m  from the centre

Explanation:

According to the law of conservation of angular momentum

We have the formula,

l0w0=Iw

I0=130+mr^2

I=130+md^2

Then substitute the values in the equation

wo= 130×w0+mr²w0=130×w+md²w

d={[130(w0-w)+mr²w0]/(mw)}^1/2

d={[130(3.00-5.00)+ 48.5×1.705²×3.00] / (48.5×5)}^1/2

d=23.4 m

The girl stopped 23.4 m  from the centre