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(8 pts) A point mass of mass mp is initially at rest on a frictionless surface....

(8 pts) A point mass of mass mp is initially at rest on a frictionless surface. Someone who is bored while social distancing is making a Rube Goldberg machine for a Tik Tok video. As part of this, a long stick will swing downwards and strike the point mass, causing the stick to come to completely to rest and the point mass to be launched with a horizontal velocity vf .

The rod has a total length 2.0 m is pivoted at one end. It has a non-uniform mass density given by l = 3 + 4y,
where y = 0 at the pivot and the lowest end of the rod is at y = +2.0 m.
What is the angular speed of the rod right before it strikes the point mass? Put your answer in terms of only mp and vf.

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