This is part one of three part question, please show work and please, if you cou

Question

This is part one of three part question, please show work and please, if you could, explain why you are doing what your doing.

Description: A small block of mass m which is initially at rest, slides down without friction through height h0 and then collides with a uniform rod of the same mass m and of a length L and sticks to the end of the rod. The rod pivots about point 0 (the top of the rod) to an angle before momentarily stopping. After collision the motion of the rod and block system can be considered simple harmonic motion. In terms of L, h0 and g (9.8):

Question: Find an expression for the angular speed of the rod and block system immediately after collision.

Explanation / Answer

The speed of the block immediately before the collision is:
v = sqrt{2 g h1}
Angular momentum's conservation:
M v R = {(M/3)R² + MR²}
= 3 v/4R
Finally
(1/2) (4/3) M R² ² = M g R (1 - cos)
= sqrt{3 g (1 - cos)/2 R}

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