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 1.50 m, an initial angular speed of 3.17 rad/s, and a moment of inertia of 129 kg-m*. The mass of the person is 42.9 kg. Find the final angular speed of the carousel after the person climbs aboard the tolerance is +/-290 Click if you would like to Show Work for this question: Open Show Work

Explanation / Answer

here,

mass of person , m = 42.9 kg

moment of inertia of carousel , I = 129 kg.m^2

initial angular speed , w0 = 3.17 rad/s

radius ,r = 1.5 m

let the final angular speed be w

using conservation of angular momentum

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

129 * 3.17 = ( 129 + 42.9 * 1.5^2) * w

solving for w

w = 1.81 rad/s

the final angular speed is 1.81 rad/s

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