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Why doesn't the gravity affect the torque along the z axis?

  1. Feb 17, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-2-17_17-24-42.png

    2. Relevant equations


    3. The attempt at a solution

    I understand in general the argument of the problem, the only thing which I'm not sure of is why the gravity doesn't affect the torque. My guess is that it gets cancelled by the normal force that is applied on the axle but I'm not 100 % sure.

    Thanks !
     
  2. jcsd
  3. Feb 17, 2017 #2

    kuruman

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    Can gravity exert a torque in the z-direction?
     
  4. Feb 17, 2017 #3
    Why couldn't it ? Torque is defined as the cross product of the distance from the origin and the net force, right ?
     
  5. Feb 17, 2017 #4

    kuruman

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    Almost. Distance is a scalar, not a vector. If force ##\vec{F}## is applied at position vector ##\vec{r}##, the torque about the origin is ##\vec{r} \times \vec{F}##.

    What is the direction of the torque if the force is gravity?
     
  6. Feb 17, 2017 #5
    135 degrees in the xy plane ?
     
  7. Feb 17, 2017 #6

    kuruman

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    The angle is unimportant. What matters is that the torque is in the xy plane. In what direction is the angular momentum of the wheel?
     
  8. Feb 18, 2017 #7

    haruspex

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    And what is the angle between the vector product and each of the original vectors?
     
  9. Feb 18, 2017 #8
    It's perpendicular to both of them
     
  10. Feb 18, 2017 #9

    haruspex

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    Right. And the force of gravity is in the z direction, so any torque it exerts must be at right angles to the z direction.
     
  11. Feb 19, 2017 #10
    Ok, but I'm still not sure of understanding why torque is disregarded.
     
  12. Feb 19, 2017 #11

    kuruman

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    In what direction is the torque?
    In what direction is the angular momentum?
    What is the direction in which the angular momentum can change?
    How is the torque vector related to the change of angular momentum vector?
     
  13. Feb 19, 2017 #12

    haruspex

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    For the moment, suppose the turntable is stationary. We drop a lump of putty on one edge. This exerts a torque about a horizontal axis. Will the turntable tip? Why not?
     
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