Plz be thorough. Thanks! A small, 10.0 g insect stand at one end of a thin unifo

Question

Plz be thorough. Thanks!

A small, 10.0 g insect stand at one end of a thin uniform metal rod which is initially at rest on a frictionless horizontal table. The other end of the rod is bolted into the table, so that the rod pivots without friction. The rod has a mass of 100.0 g and is 100.0 cm long. The insect jumps in the horizontal direction, perpendicular to the rod, with a speed of 40.0 cm/s relative to the table. What is the resulting angular speed of the rod? What is the total kinetic energy of the entire system after the bug leaps? Where does this energy come from?

Explanation / Answer

Initial momentum of the system was zero.
The gain in momentum of the bug is mu
The loss in momentum of the rod gives an angular momentum to the rod = muL.
The angular momentum of the rod about one end is I? = ? *ML^2/3

Equating the two

? = 3mu / (ML) = 3*10*40/(100*100) = 0.12 rad /s
? = 0.12 rad /s

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