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When is Energy/Momentum/Angular Momentum really conserved?

  1. Nov 14, 2016 #1
    1. The problem statement, all variables and given/known data
    So during collisions between 2 point masses, I know that momentum is always conserved, but energy may or may not be conserved.
    i-4ff5e541650f789e29600e929d1c96a5-inelastic-1.jpg

    Now, in this case, where we have a block colliding with a pivoted rod, I know that angular momentum is always conserved, but neither energy or momentum is.
    5b75fdc23787492183abe2963b37f88d.png

    Now, in the last case, if I get rid of the pivot, I believe that energy, momentum, AND angular momentum are conserved.
    b58ce966cf4c4e0485e1375f2958f976.png

    Can somebody explain the conditions for which energy, momentum, and angular momentum is conserved?
    2. Relevant equations
    $KE_i = KE_f$
    $p_i = p_f$
    $L_i = L_f$

    3. The attempt at a solution

    From my understanding, it's if there are no "external forces" for momentum and angular momentum. I'm not sure about energy. However, for the 2nd case, what "external force" is there? I understand there's some force from the pivot point on the rod, but why would that be "external"? And if that were considered external, why wouldn't the force from the block on the rod be considered as "external" in the 3rd case?

    Thanks!
     
  2. jcsd
  3. Nov 14, 2016 #2

    gneill

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    Staff: Mentor

    Momentum is always conserved unless there are external forces acting.
    Mechanical energy can change in an isolated system if that system includes non-mechanical energy storage mechanisms (such as energy stored as heat or in chemical substances) or can be lost to heat due to friction or locked away in mechanically deformed materials (perhaps initially as heat which is then radiated away).
    What holds the pin in place? Can you draw a surface around your system (like a Gaussian surface) that includes the pin and everything that supports it?
    Because the block is part of your system: You're looking at the block and rod as the system.

    By the way, energy need not be conserved if the collision is not perfectly elastic. If the block sticks to the rod or if there is a non-unity coefficient of restitution for the materials there will be energy loss.
     
  4. Nov 14, 2016 #3

    haruspex

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    Science Advisor
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    Gold Member
    2016 Award

    Only if you take the pivot (or a point on the line through the pivot, parallel to the motion of the block) as the reference axis.
     
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