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Rigid Body Motion - cylinder on a plane

  1. Apr 7, 2010 #1
    1. The problem statement, all variables and given/known data
    280qk4l.jpg
    Pretty picture:
    j5f3ic.jpg

    I am currently stuck on #1.

    2. Relevant equations
    Not exactly sure but...
    For #1, I assume the relevant equations are those relating the (i) gravitational force to momentum and (ii)torque due to gravity to angular momentum:

    (i) F = dP/dt
    (ii) K = dM/dt, where K = r x F


    3. The attempt at a solution
    I don't know how to begin. I figured maybe if I find r of the center of mass, take the absolute value of the derivative with respect to time then I'll know the speed...but where do I place the coordinate system then? Or I thought, if I use the equations listed above to find the momentum and angular momentum, I could do something with those to find the speed. I just don't know, quite confused right now.
     
    Last edited: Apr 7, 2010
  2. jcsd
  3. Apr 7, 2010 #2
    Oookay, here's a more serious attempt at an answer:

    The instantaneous axis of rotation for this problem is the axis where the cylinder is in contact with the plane. So, the motion of the cylinder can be described as a rotation around this axis (not sure how to imagine this, but ok). This simplifies the problem because the distance of the center of mass from this axis is:
    [tex]\sqrt{a^2+R^2-2aRcos\phi}[/tex], where [tex]\phi[/tex] is the angle between the perpendicular from the instantaneous axis of rotation and the center of mass. Therefore, the velocity of the cylinder is:
    [tex]V = \dot{\phi}[/tex][tex]\sqrt{a^2+R^2-2aRcos\phi}[/tex].

    The immediate problem that I see with this answer is that it doesn't incorporate the moment of inertia, I, like it says it should in the question.
     
  4. Apr 7, 2010 #3

    vela

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    Your answer looks fine. Just make sure it gives you sensible results for easy-to-check cases. I'm not sure why the problem mentioned I since it's not a geometrical parameter.
     
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