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 dose 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.S6 m, an initial angular speed of 3.01 rad/s, and a moment of Inertia of 128 kg m^2. The mass of the person Is 46.1 kg. Find the final angular speed of the carousel after the person Climbs aboard.

Explanation / Answer

The angular acceleration stuff is irrelevant as we can just use conservation of angular momentum.

Initial ang. mom = I* = 128 kg.m^2 * 3.01 rad/s = 385.28 kg.m^2/s

Moment of inertia of person (a rotating point mass) is m*r^2
= 46.1kg*1.56m^2 = 71.916 kg.m^2

So the final moment of inertia is I = 128 + 71.916=199.916 kg.m^2

So f = 385.28 / 199.916 rad/s = 1.93 rad/s

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