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Cross Product problem

  1. May 6, 2012 #1
    Background: we're trying to show that the rate of change of angular momentum of an object about its center of mass (position given by R) is equal to the total torque about R.

    Why are the terms in red equal to 0? If anything, shouldn't the terms circled in in blue be equal to zero since the vectors R and ai are parallel and ri` and ai` are parallel?

    Thank you!
     

    Attached Files:

  2. jcsd
  3. May 7, 2012 #2

    tms

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    What would it mean if, as you say, the acceleration of each individual particle were parallel to [itex]\vec R[/itex]?
     
    Last edited: May 7, 2012
  4. May 7, 2012 #3
    Then there is no angular momentum and only linear momentum?

    EDIT: actually i made an error with my question. the new image is attached.
    If ri` and ai` are parallel, shouldn't the cross-product be 0? So in the last line, the Ʃ miri` × A would be left instead?
     

    Attached Files:

  5. May 7, 2012 #4

    tms

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    No. Reexamine your assumption.

    Why do you think they are parallel?
     
  6. May 7, 2012 #5
    Isn't a the double derivative of r (so they are parallel)?
    Thanks again!!
     
  7. May 8, 2012 #6
  8. May 9, 2012 #7

    tms

    User Avatar

    That doesn't mean they must be parallel. If it did, it would mean that you could change the forces on an object just by moving the origin of the coordinate system.
     
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