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YoYo rolling on ground! (checking work mostly)

  1. Nov 27, 2008 #1
    1. The problem statement, all variables and given/known data

    See post #3 Assume the YoYo is a solid cylinder with mass M and radius R for all parts!!!!!

    2. Relevant equations

    Lots?

    3. The attempt at a solution

    Part A - Find the moment of inertia about the center of mass and the point of contact with the ground:

    ICOM = 1/2 MR2
    IIPoC = 1/2 MR2 + MR2 = 3/2 MR2 by parallel axis theorem

    Part B - Calculate the torque on the Yoyo about the center of mass, and the net horizontal force.

    Torque = r x F = rF since r is perp to F
    Fnet x = F cos θ

    Part C - What is the angular accel. of the yoyo about its center of mass? Linear acceleration?

    Torque = rF = Iα α = rF/I α = 2rF/MR2

    and since alin = αr
    a = 2r2F/MR2

    Part D - Find the net torque about the instantaneous point of contact

    Ok heres where I get stuck. Torque = rF sin σ , where σ is the angle between the applied force F and the r vector, right? Well no joke the geometry is complex. I cant find any way to get the angle between these two, here's what I've got so far:
    [​IMG]

    σ is the angle between the two blue lines, which represent the force and the r vector. Ive also extended the force line so you can see the line of action, if it helps.

    Any help would be greatly appreciated!
     
    Last edited: Nov 27, 2008
  2. jcsd
  3. Nov 27, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Can you at least describe the problem and what you are asked to find.
     
  4. Nov 27, 2008 #3
    The picture you see above is the bottom half of a YoYo of mass M. The inner axle has a radius r and the outer radius is R. The string is wrapped under the axle and being pulled gently so the YoYo rolls to the left without slipping.

    [​IMG]

    Im asked to find the net Torque on the YoYo about the instantaneous point of contact with the surface. Trouble is I cant find the angle between the vectors, which is what the above diagram is trying to accomplish.
     
  5. Nov 27, 2008 #4

    Doc Al

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    Staff: Mentor

    With a bit of trig you should be able to find the coordinates of the point of application of the force, thus you can find the position vector of the force and the angle it makes with the horizontal.
     
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