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Conservation of angular momentum

  1. Jun 16, 2012 #1
    1. The problem statement, all variables and given/known data
    There's a system of 4 masses, all connected to a cross which has a negligible mass, and which is positioned on a smooth surface. The distance of each mass from the center of the cross is L and the cross spins around its center in a constant radial velocity of ω0 rad/sec:
    dPcyf.gif
    Now mass m4 disconnects from the cross.

    What is the the radial velocity of the system after m4 disconnected, considering m1=m3 and m2=m4=M?

    2. Relevant equations
    Conservation of momentum:
    Ʃmivi=0

    Conservation of angular momentum:
    Ʃmiviri=ωI

    3. The attempt at a solution
    I calculated using conservation of momentum that the linear velocity of the system after m4 disconnected was v2=Mω0L/(M+2m)

    Now I think I should use the law of conservation of angular momentum but I'm not sure how. I think that the center of mass is L/2 to the right from the center of the cross so the distance of m1 and m3 from the center of mass is √((0.5L)2+L2). What should I do next?
     
  2. jcsd
  3. Jun 16, 2012 #2
    Relevant equations

    Moment of Inertia =?
    Angular Momentum=?
     
  4. Jun 16, 2012 #3
    I know that the moment of inertia is I=Ʃmiri2 and the angular momentum L can be expressed as ωI, so I tried:

    L=Ʃmiviri=ωI = ω(Ʃmiri2) and I can get the value of ω this way, but I'm not sure what the the distance from each mass to the center of mass is. I mean, what are the values of ri in this sum: Ʃmiri2 ?
     
  5. Jun 17, 2012 #4
    You have to start with conservation of energy.
    All masses have equal tangential velocity.
    As mass m4 detached from the cross(it follows a tangential path), the total energy of the system remains.

    Using consevation of momentum requires the momentum of detached mass m4, which follows a straight line.
     
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