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?

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Physics

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4 September, 13:02

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?

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Answers (1)

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Cristofer French · 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