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Find the Angular Acceleration, acceleration and friction force extered

  1. Apr 28, 2013 #1
    1. The problem statement, all variables and given/known data
    The circular disk of 595-mm radius has a mass of 16 kg with centroidal radius of gyration = 500 mm and has a concentric circular groove of 220-mm radius cut into it. A steady force T is applied at an angle θ to a cord wrapped around the groove as shown. If T = 41 N, θ = 39°, μs = 0.23, and μk = 0.19, determine the angular acceleration α of the disk, the acceleration a of its mass center G, and the friction force F which the surface exerts on the disk. The angular acceleration α is positive if counterclockwise, negative if clockwise; the acceleration a is positive if to the right, negative if to the left; and the friction force F is positive if to the right, negative if to the left.

    I have attached an image of the question

    2. Relevant equations

    rs is the smaller radius of 220 mm

    rL is the larger radius of 595 mm

    I = k2
    m
    3. The attempt at a solution

    I started off by drawing a FBD of the circular disk, in which I included the forces of T, mg, N (normal force) and F (friction force)

    ƩFx: max = Tcos(θ) - F

    ƩFy: may = Tsin(θ) - mg + N

    ƩMG: IGα = Trs - FrL

    So, now I have three equations but 5 unknowns: ax, ay, F, N and α. How do I find the other two equations?

    EDIT:

    I've just realized that ay = 0. So, could I use F = u*N, where u would be the kinetic of static friction, as the fourth equation?
     

    Attached Files:

  2. jcsd
  3. Apr 28, 2013 #2
    Yeah, I jumped the gun a bit.

    It looked more complicated than it was. I've solved it now. Thanks
     
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