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Rotational kinematic need explanation

  1. May 30, 2015 #1
    • ice skater with mass = 80 kg
    • moment of inertia (about her central axis) 3 kg m2.
    • Catch baseball with outstretched arm 1m from her central axis.
    • Ball has mass 0.3 kg and v0 = 20 m/s before the catch.
    • V system ( skater + ball ) after catch = 0.0747 m/s
    Question :
    b. Angular speed of the system (skater + ball) after the catch ?
    c. Percent Kinetic Energy lost during catch ?

    Solution :
    http://imgur.com/fj0Xstv
    Is it correct ( answer for question c) ?

    If yes, why K0 or kinetic energy before the catch doesn't have rotational kinetic energy ?
    Ball has ω0 so it have rotational kinetic right ?
     
  2. jcsd
  3. May 30, 2015 #2
    This solution assumes that V is the centre mass velocity after plastic collision. Angular momentum principle need because kinetic energy take not only for V, we have and rotation.

    Angular momentum depends from the origin, so used only for the centre mass system.
     
  4. May 30, 2015 #3
    Thank you for your responese ,mihos.
    o_O so is it correct the answer for question c ?

    what is the answer for this one :
    why K0 (in solution c) or kinetic energy before the catch doesn't have rotational kinetic energy ?
    Ball has ω0 so it have rotational kinetic right ?
     
  5. May 31, 2015 #4

    haruspex

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    I think the solution is not perfectly accurate because it treats the skater's mass centre as an inertial frame for the angular momentum calculation. I'll check later to see if that changes things. But let that pass for now.
    You can view the ball has having linear KE or as having rotational KE about the skater's mass centre, but not as having both.
     
  6. May 31, 2015 #5
    Why not ? i'm confused.
    How can ball that have both angular and linear speed only have 1 KE ?
    Formula for KE = linear KE + rotational KE ? right ?
    or is it because the ball is in the air so it can't roll (so no rotational movement)?

    Thanks
     
  7. May 31, 2015 #6

    haruspex

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    You have no evidence that the ball is rotating on its own axis, and even if it were it would only be relevant if spinning on a vertical axis, and even then would have negligible result on the skater's rotation.
     
  8. May 31, 2015 #7
    Ball has ω0 = 20 rad/s , isn't that mean that the ball rotate ?
    Also the ball has moment of inertia so that means it rotate on its central axis right ?
    :bow:
     
  9. May 31, 2015 #8

    haruspex

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    That's its rotation about the skater's axis just as the skater is about to catch it, not about its own axis.
    I would not have written the solution this way. Instead of writing in terms of the ball's angular velocity about the skater I would have referred ti its angular momentum. A key difference is that the angular velocity increases until the ball is at its closest point to the skater's axis, whereas the angular momentum is constant until then. It might have confused you less.
     
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