# Find the Angular Acceleration, acceleration and friction force extered

1. Apr 28, 2013

### Northbysouth

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:

• ###### dyn 6.089.png
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2. Apr 28, 2013

### Northbysouth

Yeah, I jumped the gun a bit.

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