A 25 kg girl stands on the edge of a merry go round that is turning with an angu

Question

A 25 kg girl stands on the edge of a merry go round that is turning with an angular speed of .75 rad/s. the merry go round has a radius of 2.5 m and a moment of inertia of 200 kg m^2. The girl the walks directly toward the axis of the merry go round and stands at the center. What is the new angular speed of the merry go round? A 25 kg girl stands on the edge of a merry go round that is turning with an angular speed of .75 rad/s. the merry go round has a radius of 2.5 m and a moment of inertia of 200 kg m^2. The girl the walks directly toward the axis of the merry go round and stands at the center. What is the new angular speed of the merry go round?

Explanation / Answer

here,

mass of girl , m = 25 kg

initial angular speed , w0 = 0.75 rad/s

r = 2.5 m

I = 200 kg.m^2

let the final angular speed be w

using conservation of momentum

( I + m * r^2) * w0 = I * W

( 200 + 25 * 2.5^2) * 0.75 = 200 * w

w = 1.34 rad/s

the angular speed is 1.34 rad/s

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