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Torque, radius, force a common experiment in physics

  1. Mar 4, 2008 #1
    1. The problem statement, all variables and given/known data

    A common physics demonstration consists of a ball resting at the end of a board of length L that is elevated at an angle of theta with the horizontal. A light cup is attached to the board at Rc (Rc is a distance up the board from the bottom, it is not past the support stick) so that it will catch the ball when the support stick is suddenly removed. a) show that the ball will lag behind the falling board when theta < 35.3 and b) the ball will fall into the cup when the board is supported at this limiting angle and the cup is placed at
    Rc = (2L)/(3cos(theta))

    2. Relevant equations

    F*r*sin([tex]\theta[/tex]) = [tex]\tau[/tex]

    3. The attempt at a solution

    We did this in class today actually, and I know this experiment works because of the torque involved. That is, because the stick has a radius of l, the end of it will fall faster than the ball, which doesn't have any sort of torque to speak of. The longer a stick, the faster the end moves when the other end is moved even slightly, basically. But while that's a fine English-based answer, I need something more...mathematical, and I don't really know how to approach this one mathematically.
     
  2. jcsd
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