A carousel has a radius of 1.70 m and a moment of inertia of 110 kg · m2. A girl of mass 44.0 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.40 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 5.4 rad/s. How far from the center, in meters, did the girl stop?

Question

Physics

Ezra Khan

30 June, 16:17

A carousel has a radius of 1.70 m and a moment of inertia of 110 kg · m2. A girl of mass 44.0 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.40 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 5.4 rad/s. How far from the center, in meters, did the girl stop?

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Answers (1)

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Macey Mckay · Answer 1

Initial moment of inertia of the carousel + girl

I₁ = 110 + 44 x 1.7²

= 110 + 127.16

= 237.16 kgm².

final moment of inertia of carousel + girl

I₂ = 110 + 44 x d²

applying law of conservation of angular momentum

I₁ ω₁ = I₂ω₂

ω₁ and ω₂ are angular velocities of the carousel before and after.

237.16 x 3.4 = (110 + 44 x d²) x 5.4

806.34 = 594 + 237.6 d²

237.6 d² = 212.34

d²=.8936

d =.9453 m