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Angular Velocity Of A Wheel

  1. Nov 13, 2011 #1
    1. The problem statement, all variables and given/known data
    A wad of sticky clay with mass 2.45 kg and velocity vi = 52.0 m/s is fired at a wheel of moment of inertia 1.2 kg m2 and radius R = 1.26 m. The wheel is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at distance d = 0.842 m from the center.
    Find the angular speed of the cylinder (in rad/s) just after the clay strikes and sticks to the surface of the wheel.


    2. Relevant equations

    T=rF=Iα.


    3. The attempt at a solution
    I don't have a text book with me so I am trying to work through this by searching the internet and my memory. I am thinking in order to solve this you would just take the angular force times the radius and you would have torque. Then from there you would find the angular speed from the torque but I don't see how you would find the torque if the problem only gives you the velocity of the clay projectile.
     
  2. jcsd
  3. Nov 13, 2011 #2

    Doc Al

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    Since you don't have information of the forces involved, see if you can apply a conservation law to solve the problem.
     
  4. Nov 13, 2011 #3
    Right as I finished typing I thought of conservation of momentum but isn't the clay piece an external force?
     
  5. Nov 13, 2011 #4
    Meaning the momentum is not conserved from the initial state of the wheel to the final state.
     
  6. Nov 13, 2011 #5

    Doc Al

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    While the momentum of either one--clay piece or wheel--isn't conserved by itself, the momentum of the system (the angular momentum) is.
     
  7. Nov 13, 2011 #6
    Oh okay! So does would the initial momentum of the clay equal mvd?
     
  8. Nov 13, 2011 #7

    Doc Al

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    No. You must use the distance between the line of motion of the clay and the axis of rotation.
     
  9. Nov 13, 2011 #8
    Which is d in this problem. Thanks for you help.
     
  10. Nov 13, 2011 #9

    Doc Al

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    Ah, yes it is. :wink:
     
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