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Homework Help: Why isn't linear momentum conserved?

  1. Mar 22, 2012 #1
    A ball of mass m elastically collides with a uniform rod of length L and mass 2m that is pinned at its center.

    Which is/are conserved?

    A. Angular Momentum
    B. Linear Momentum
    C. Kinetic Energy
    D. A/C
    E. All

    The answer is D. Can someone explain why angular momentum is conserved and linear momentum isn't?
  2. jcsd
  3. Mar 22, 2012 #2


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    Because the momentum of whatever the rod is pinned to (say the earth) is being ignored. The pin applies a force to something that isn't included as part of the problem statement.
  4. Mar 22, 2012 #3
    Sorry, I may have an incorrect understanding of what exactly the linear momentum and angular momentum of a system are. Do you mind briefly explaining those as well?
  5. Mar 22, 2012 #4
    What does A/C mean? o_O
  6. Mar 22, 2012 #5
    angular momentum is always conserve for collisions that do not involve external torques (i remembered my prof and tiny-tim saying something like that )

    so the angular momentum of the horizontally moving ball, with respect to say the center of the rod , will be conserved as the angular momentum of the rod rotating as a result of the impact.

    since the rod is pinned at the center, it has no translational movement, i.e it can't move horizontally. thus if the ball has linear momentum ( horizontal), then it will not be conserved because the rod doesn't move horizontally, its center of mass is fixed.
  7. Mar 22, 2012 #6
    A/C means option A and C are correct :D
  8. Mar 23, 2012 #7


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    The linear momentum of a system is conserved if there are no external forces acting on the system. Since the pin exerts a force on the rod during the collision, linear momentum is not conserved.

    Or ... you could consider the pin-plus-Earth as another rigid body that is part of the system -- as rcgldr suggested -- then linear momentum is conserved, however the momentum of Earth has not been included in calculating the momentum of the system.
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