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Angular momentum and moment of inertia

  1. Mar 29, 2016 #1
    1. The problem statement, all variables and given/known data

    Hi everyone! I'm preparing an exam and reviewing some old problems until then, to clear up some misconceptions I might have!
    A stiff massless bar is frictionless rotatable about a point O. Two mass points m1 and m2 are fixed at its ends, respectively at distances d1 and d2. The bar is at rest, when a point-shaped bubble gum hits the mass m2 perpendicularly with velocity v and sticks on it. (see attached picture) What is the angular velocity of the bar after the collision? Justify your answer. (There is no field of gravity to consider here)

    2. Relevant equations

    Moment of inertia, angular momentum

    3. The attempt at a solution

    So when I see a collision with a fixed rotatable object I think immediately angular momentum:

    m⋅v⋅d2 = Isystem⋅ω

    The left side describes the motion of the gum relative to O before the collision, while the right side describes the rotation of the system after the gum stuck on m2.

    ⇒ ω = m⋅v⋅d2/Isystem

    Since the bar is massless, I believe the moment of inertia can be calculated like for two atoms orbiting a point:

    Isystem = m1⋅d12 + (m2 + m)⋅d22

    Is that right? If so, my answer would then be:

    ω = m⋅v⋅d2/(m1⋅d12 + (m2 + m)⋅d22)

    That is all? I am surprised because usually the problems to solve are quite tough.

    Extra question: I also tried to solve that with conservation of energy, which gives a different result. But then I thought that in an inelastic collision, there is some loss of energy due to the fact that the gum sticks on the ball, so it can't apply here. Is that assumption correct?

    Thank you very much in advance for your answers.

    Julien.
     

    Attached Files:

    Last edited: Mar 29, 2016
  2. jcsd
  3. Mar 29, 2016 #2

    TSny

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    Homework Helper
    Gold Member

    Looks good except for your calculation of Isystem. Should anything be squared there?
    I agree with your comments about energy.
     
  4. Mar 29, 2016 #3
    Oops yeah I forgot to write the squares, but they are on my paper. I edit the post immediately, thank you for your answer!
     
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