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Math Help - ball hitting a swinging rod

  1. #1
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    ball hitting a swinging rod

    A thin uniform metal bar, 2m long and weighing 90N, is hanging vertically from the ceiling on a frictionless pivot. Suddenly, it is struck 1.5m below the ceiling by a small 3kg ball, intially travelling horizontally at 10m/s. The ball rebounds in the opposite direction with a speed of 6m/s.
    Find the angular speed of the bar after the collision.

    I am struggling to find the right energy/conservation equation to use. I know it is to do with the conservation of angular momentum, but i cannot see how to use the fact that the small ball rebounds with a speed 6m/s in my equation.
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  2. #2
    A Plied Mathematician
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    I would recommend two things:

    1. Look at the ball as part of the system, contributing to the angular momentum. If you consider the ball immediately before and immediately after the collision, you will be able to view it its motion as approximately rotational, just as the motion of the free end of the bar is initially going to be approximately linear.

    2. Your conservation of angular momentum equation is, I think, the way to go. You'll have the following:

    I_{\text{ball}}\,\omega_{\text{ball},i}=I_{\text{b  all}}\,\omega_{\text{ball},f}+I_{\text{bar}}\,\ome  ga_{\text{bar},f}.

    Does that give you a nudge? What's your target variable?
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