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Angluar Momentum and Torque

  1. Mar 4, 2007 #1
    Hi, I have no idea how to do this problem, wondering if anyone can help:

    Two identical spheres, each of mass M and negligible radius, are fastened to opposite ends of a rod of negligible mass and length 2l. This system is initially at rest with the rod horizontal and is free to rotate about a frictionless, horizontal axis through the center of the rod and perpendicular to the plane of the page. A bug of mass 3M, lands gently on the sphere on the left. Assume that the size od the bug is small compared to the length of the rod. Express your answers to all parts of the question in terms of M, l, and physical constants.

    a.) Determine the torque about the axis immediately after the bug lands on the sphere.

    b.) Determine the angular acceleration of the rod-spheres-bug system immediately after the bugs lands.

    Then later on in the problem, it states: The rod-sphere-bug system swings about the axis. At the instant that the rod is verticle determine each of the following:

    c.) The angular speed of the bug.

    d.) The angular momentum of the system

    e.) The MAGNITUDE and DIRECTION of the force that must be exerted on the bug by the wphere to keep the bug from being thrown off the sphere.




    So, I know that Torque = r * F or Torque = I * omega for part "a", but passed that I don't know where to go because I don't know what the force "F" would be and I'm not given the moment of inertia or angular velocity...

    I'm really confused...




    Thanks in advance for the help!
     
    Last edited: Mar 4, 2007
  2. jcsd
  3. Mar 4, 2007 #2

    Doc Al

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    Staff: Mentor

  4. Mar 4, 2007 #3
    Thanks for the freebie...but it doesn't help me with part A. After that, I think I might be able to do it.
     
  5. Mar 4, 2007 #4

    Doc Al

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    What forces act on the system? What torques do they exert about the axis?
     
  6. Mar 4, 2007 #5
    The force of the bug-sphere on the entire system.

    So, is it right to do Net Force = ma, then: F + mg = ma, where F is the force of the bug on the sphere. Then I got F = mg = 4Mg for the sphere with the bug. The one without the bug is just Mg. From there I did Torque = r x F, and got 4Mgl - Mgl = 3Mgl.

    Is that how it's supposed to be done though, or was it just good guessing because in the figure, they show the bug landing on the side of the sphere and not on the top, which I thought would effect the F = ma process?
     
  7. Mar 4, 2007 #6

    Doc Al

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    The bug lands gently on the sphere, so the only force you need to worry about is gravity.

    Since the radii of the spheres are negligible, it doesn't matter where the bug lands.
     
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