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Turning Force vs. Accelerating Force

  1. Dec 17, 2008 #1
    If I have a sphere (or another 3D object) and I apply a force to it through the centre of gravity, it will accelerate according to F=ma
    If I apply a force to the sphere which doesn't act through the centre of gravity, I apply a turning force according to T=F*d

    How do you figure out how much the body as a whole accelerates when you apply a turning force to it?
  2. jcsd
  3. Dec 18, 2008 #2


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    Staff Emeritus
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    Gold Member

    Simply apply Newton's second law and well as the rotational equation of motion. Newton's second law is still valid even if a the force is not applied through the COM of the body.
  4. Dec 18, 2008 #3
    But does applying a force to the edge of an object have the same accelerating effect?
    I imagine that a glancing blow won't move an object as much as a force acting through the COM
  5. Dec 18, 2008 #4

    D H

    Staff: Mentor

    Yes, it does. It seems a bit counterintuitive, but that's how things work. This has been very well tested -- e.g., in spacecraft.
  6. Dec 18, 2008 #5
    That is counter-intuitive. So, on this diagram, all three equal magnitude forces will accelerate the block the same amount in the same direction? (And two will cause it to rotate?)

  7. Dec 18, 2008 #6

    D H

    Staff: Mentor

    That's correct.
  8. Dec 18, 2008 #7


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    The forces are the same, but not the power. The forces that that cause rotation (angular acceleration) have to be applied at a faster rate of acceleration, at faster speed, and longer distance, so more work (force times distance) is done for the forces that cause rotation, which is why the power is higher, and the total energy, linear and angular, is increased more by the forces that also cause rotation (angular acceleration).
  9. Dec 19, 2008 #8
  10. Dec 19, 2008 #9

    D H

    Staff: Mentor

    How is that thread related at all? That thread is about particles: Point masses. This thread is about what happens to a non-point mass object subject to a force that does not pass through the object's center of mass.
  11. Dec 22, 2008 #10
    This question is related to my above question. Friction doesn't act through the center of mass, but then where on a free body diagram do you place the force which keeps the object (say a block) from spinning?
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