A homogeneous rod AB of length L = 1.8 m and mass M is pivoted at the center O in such a way that it can rotate it can rotate freely position. An insect S of the same mass M falls vertically with speed V on the point C, midway between the points O and B. Immediately after falling, the insect moves towards the end B such that the rod rotates with a constant angular velocity omega. (a) Determine the angular velocity `omega` in terms of V and L. (b) If the insect reaches the end B when the rod has turned through an angle of `90^@`, determine V.

A homogeneous rod AB of length L = 1.8 m and mass M is pivoted at the

1.	A homogeneous rod AB of length L = 1.8 m and mass M is pivoted at the center O in such a way that it can rotate it can rotate freely position. An insect S of the same mass M falls vertically with speed V on the point C, midway between the points O and B. Immediately after falling, the insect moves towards the end B such that the rod rotates with a constant angular velocity omega. (a) Determine the angular velocity `omega` in terms of V and L. (b) If the insect reaches the end B when the rod has turned through an angle of `90^@`, determine V.
Answer» Let the angular velocity be `omega`, when the insect strikes the rod at `C`. By the conservation `OhatI` angular momentum about `C` `Mv(L)/(4)=I_(0)omega=[(ML^2)/(12)+M((L)/(4))^(2)]omega` `=(7)/(48)ML^(2)omega` `omega=(12v)/(7L)`

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