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GRE question - angular momentum

  1. Sep 7, 2009 #1
    1. The problem statement, all variables and given/known data
    A uniform stick of length L and mass M lies on a frictionless horizontal surface. A point particle of mass m approaches the stick with speed v on a straight line perpendicular to the stick that intersects the stick at one end as shown in the attached image. After the collision, which is elastic, the particle is at rest. What is the speed, V, of the center of mass of the stick after the collision.

    a) (m/M)*v
    b) m/(m+M)*v
    c) sqrt(m/M)*v
    d) sqrt(m/(m+M))*v
    e) (3m/M)*v

    2. Relevant equations
    Ki = Kf
    Li = Lf = I*w = mvr
    Pi = Pf

    3. The attempt at a solution
    So I've solved this problem using linear momentum. I said mv = MV. and I get V = (m/M)*v. This is the correct answer. (choice a)

    But I cannot for the life of me, solve this using angular momentum and I was hoping I could get some help with that.

    First, using angular momentum:
    I said that right before the collision the the angular momentum of the particle is mv(L/2) (relative to the center of mass of the stick). Then after the collision, the angular momentum of the center of mass is I*w.

    I initially set those two expressions equal to one another and solve but that doesn't give me the correct answer.

    I think I'm leaving out a term, but I don't know what it is or how to find it.

    Thank you very much!

    Attached Files:

  2. jcsd
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