A thin rod has a length of 0.796 m and rotates in a circle on a frictionless tab

Question

A thin rod has a length of 0.796 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 0.517 rad/s and a moment of inertia of 1.22 x 10-3 kg·m2. A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod?

I got an answer of 0.14367 rad/s, but it's incorrect. Why?

Explanation / Answer

Applying angular momentum conservation,

Li = Lf

(1.22 x 10^-3) (0.517) = ( (1.22 x 10^-3) + (5 x 10^-3 x 0.796^2)) wf

wf = 0.144 rad/s

change in w = wf - wi

= 0.144 - 0.517

= 0.373 rad/s

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