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Solid Sphere,Impulse

  1. May 20, 2012 #1
    1. The problem statement, all variables and given/known data

    A uniform solid sphere has radius R and mass M. It is initially at rest but is
    free to move, floating in space with nothing touching it. It suddenly receives
    an impulse J at a tangent to its surface.

    As a function of R, M and J, find formulae for:

    (a) the linear velocity of the sphere,
    (b) its angular velocity around its centre of mass
    (c) its total kinetic energy after the impulse.




    2. Relevant equations
    L=Iω,J=MV,V=ωR


    3. The attempt at a solution

    a) All particles on the sphere have the same angular velocity and different linear velocities depending on their distance from the centre.

    J=ΔP=M(V-u)=MV so V=J/M Whose velocity is this ? ( V=J/M) .Is it the C.o.M ?

    b) L=Iω <=> ω=L/I = 5L/(2MR2) But how can i move from here ?

    c) well if i knew how to solve b) then c) is an easy one !
     
  2. jcsd
  3. May 20, 2012 #2

    Doc Al

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    Staff: Mentor

    Good. That's the velocity of the COM.

    What's the angular impulse?
     
  4. May 20, 2012 #3
    ΔL=IΔω but since it was stationary at first then ΔL=Iω

    It seems to be simple but i still can't understand how to relate these two :S
     
    Last edited: May 20, 2012
  5. May 20, 2012 #4
    Actually no :S
     
  6. May 20, 2012 #5

    Doc Al

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    Staff: Mentor

    Nothing wrong with that, but what is ΔL in terms of J?
     
  7. May 20, 2012 #6
    Hmm dL=Iω=J*R=MVR but i realized that V=ωR is not valid , why is that ?
     
  8. May 20, 2012 #7

    Doc Al

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    Staff: Mentor

    The angular impulse is J*R. Now you can solve for ω.

    As to whether V = ωR is valid, that depends on what you mean by V. (In any case, you don't need it here.)
     
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