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 1.59 m, an initial angular speed of 3.41 rad/s, and a moment of inertia of 121 kg·m2. The mass of the person is 46.8 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 angular momentum = I* = 121 kg.m^2 x 3.41 rad/s = 412.61 kg.m^2/s

Moment of inertia of person (a rotating point mass) is m*r^2

I = 46.8kg x 1.59^2 = 118.32 kg.m^2

So the final moment of inertia is I = 121 + 118.32 = 239.3 kg.m^2

So f = 412.61 / 239.3 rad/s = 1.7242 rad/s

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