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Angular Momentum Torque

  1. May 4, 2012 #1
    1. The problem statement, all variables and given/known data

    Considering the concepts of Rigid Body/Angular Momentum/Torque
    A body rotating with respect to an axis that passes through ANY point P, whose acceleration could be different to zero.

    Prove:

    Ʃτ(ext, p) = dL(rel_p)/dt + ρ(cm) x Ma(p)
    Ʃτ(ext, p) = dL(rel_cm)/dt + ρ(cm) x Ma(cm)


    2. Relevant equations

    T = dL/dt
    L = Ʃ ρ x mv

    3. The attempt at a solution
    Considering a Rigid Body/Angular Momentum/Torque

    We know that Torque(ext) = dL/dt

    Now with respect to stationary point S:
    L(s, cm) = Ʃ(ρi x mivi)
    and that dL(cm)/dt = Ʃτ(ext, CM)

    Now with respect to ANY point, P, that is accelerating:
    L(s,p) = L(cm) + ρ(cm) x Mv(cm)

    after this I don't know how to prove what they are asking me for
     
  2. jcsd
  3. May 4, 2012 #2

    D H

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    Staff Emeritus
    Science Advisor

    The motion of a rigid body can be described as a combination of linear translation/acceleraion of some point plus a rotation/rotational acceleration about an axis passing through that point. So what is that "some point"? It can be any point whatsoever -- and that is what you are being asked to prove.
     
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