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 3.09 rad/s, and a moment of inertia of 121 kg·m2. The mass of the person is 41.8 kg. Find the final angular speed of the carousel after the person climbs aboard.

Explanation / Answer

The initial angular momentum is L = I = (121 kg-m2)(3.09 s-1) = 373.89 kg-m2/s

The moment of inertia of the person once on the carousel is mr2 = (41.8 kg)(1.5 m)2 = 94.05 kg-m2

that gets added to I for the carousel for a total moment of inertia of 215.05 kg-m2

But angular momentum is conserved, so the new is = L/I = (373.89 kg-m2/s)/(215.05 kg-m2)

= 1.74 rad/s

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