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Interactive Solution 9.63 illustrates one way of solving a problem similar to this one. A thin...

Interactive Solution 9.63 illustrates one way of solving a problem similar to this one. A thin rod has a length of 0.594 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 0.673 rad/s and a moment of inertia of 1.37 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?

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Answer #1

Initial moment of inertia of the system (rod+bug) with bug at the axis, = 1.37 x 10-3 kg m2

Initial angular velocity, = 0.673 rad/s

Final moment of inertia of the system (rod+bug) with bug at the other end of rod, , where, is mass of bug and is the length of rod.

Initial angular velocity, = ?

By, Law of conservation of angular momentum,

Thus, change in angular velocity

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