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Dynamics of Rotational motion

  1. Nov 14, 2006 #1
    It looks like your standard matchbox car loop.

    I need to find the minimum height h that will allow a solid cylinder of mass m and radius r_1 to loop the loop of radius r_2. "Express h in terms of the radius r_2 of the loop."

    I am not quite getting a certain portion of this. I know the important part of this problem is when the cylinder is at the top of the loop.
    Now, at this point, I know it has a potential energy of 2*r_2*m*g
    To stay on the track without slipping, I think I need v = R*omega
    At the top part of the track, the cylinder is upside down, and has no normal force... so weight matters?

    I may need to use this: K = 1/2Mv_cm^2 + 1/2 I_cm*omega^2

    mgh = (2)r_2(mg) + KE? + ?

    I am a bit confused at this point. How am I suppose to put this together?
  2. jcsd
  3. Nov 14, 2006 #2
    You are correct in that the "important part of this problem is when the cylinder is at the top of the loop".

    Hint -- draw a free body diagram for the system at that location.
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