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Northbysouth
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Homework Statement
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
Homework Equations
rs is the smaller radius of 220 mm
rL is the larger radius of 595 mm
I = k2
m
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?