A playground carousel is rotating counterclockwise about its center on frictionl

Question

A playground carousel is rotating counterclockwise about its center on frictionless bearings. A person standing still on the ground grabs onto one of the bars on the carousel very close to its outer edge and climbs aboard. Thus, this person begins with an angular speed of zero and ends up with a nonzero angular speed, which means that he underwent a counterclockwise angular acceleration. The carousel has a radius of 1.58 m, an initial angular speed of 3.08 rad/s, and a moment of inertia of 128 kg·m2. The mass of the person is 43.2 kg. Find the final angular speed of the carousel after the person climbs aboard.

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Explanation / Answer

Moment of inertia of the carousel, I1 = 128 kg.m^2 Radius of the carousel, r = 1.58 m Mass of the person, m = 43.2 kg Moment of inertia of the person, I2 = m r^2 = 43.2 * 1.58^2 = 107.8 kg.m^2 Initial angular velocity of the carousel, w = 3.08 rad/s Final angular velocity of carousel and person, w' = ? According to the law of conservation of momentum, Final angular momentum = Initial angular momentum ( I1 + I2 ) w' = I1 w ( 128 + 107.8 ) * w' = 128 * 3.08 w' = 1.67 rad/s Angular velocity of carousel + person, w' = 1.67 rad/s

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