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Homework Help: Angular velocity and acceleration of a plank

  1. Jun 24, 2017 #1
    1. The problem statement, all variables and given/known data
    A horizontal plank with a frictionless axis of rotation at its center has a large mass at one end and a small mass at the other end. It is held stationary and then released from rest. As the plank rotates (and before one end hits the ground), the magnitude of the angular acceleration of the plank (increases/decreases/or remains constant) and the magnitude of the angular velocity (increases/decreases/or remains constant) ?

    2. Relevant equations
    τ=I α
    τ=r F_perp

    3. The attempt at a solution
    The solution to this problem is that τ=I α, therefore if torque decreases, then angular acceleration increases. Thus the magnitude angular velocity must be increasing, because the angular acceleration is nonzero.

    However, I can't seem to figure out why the torque is decreasing in this problem. I know that τ=r F_perp, but how can I apply this to the problem? The lever arm obviously stays the same length. So is the perpendicular force decreasing because after the plank tilts downwards, the force of gravity downwards has both a horizontal component and a vertical component with respect to the plank (force of gravity stays the same)?

    Thanks for reading! Any help is appreciated
  2. jcsd
  3. Jun 24, 2017 #2

    Doc Al

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    Staff: Mentor

    Usually the "lever arm" is defined as the perpendicular distance from the line of force to the axis of rotation. So by that definition, the lever arm decreases.

    The length of the plank doesn't change, so I suspect that's what you meant.
    Right. The component of the weight perpendicular to the plank decreases, so the torque decreases.
  4. Jun 24, 2017 #3
    Ok, that makes sense. Thanks for the help!

  5. Jun 25, 2017 #4


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    Science Advisor
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    Check that.
  6. Jun 25, 2017 #5
    What do you mean?
  7. Jun 25, 2017 #6
    Oops never mind. I meant if torque decreases, angular acceleration decreases
  8. Jun 25, 2017 #7

    Doc Al

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    Staff: Mentor

    I had assumed you just messed up that sentence, since what followed didn't depend on it. (Otherwise I would have said something.)
  9. Jun 25, 2017 #8
    Yeah, just a typo. Thanks for all the help!
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