A thin rod has a length of 0.25 m and rotates in a circle on a frictionless tabl

Question

A thin rod has a length of 0.25 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.30 rad/s and a moment of inertia of 1.40 10-3 kg · m2. A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (mass = 4.2 10-3 kg) gets where it's going, what is the angular velocity of the rod?


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Explanation / Answer

I of the rod = Irod = 1.4 x 10^-3

initial angular velocity = .3 rad/s

initial angular momentum = I = .42 x 10^-3

when the bug goes to other end

moment of inerital of the bug =mL^2

using conservation of angular momentum

.42 x 10^-3 = (1.4 x 10^-3 + 4.2 x 10^-3 * .25^2)'

' = .2526 rad/s

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