Thanks for the welcome!
Yes, it sounds weird, but it's only a homework-like question. This is actually for a project I'm working on, not a homework problem for a class. According to the guidelines, this was the best forum to place it in. I just tried to list out all the knowns, unknowns and assumptions that are relevant.
The end equation will be:
T = 200 in-lbs
[tex] μ_s = T/(N*x) [/tex]
I'm trying to determine suitable materials for varying applied normal forces, so with different normal forces, the μs will change to keep the final equation balanced. In addition, each radius will alter the curves on the graph and I expect it'll bring the μs values lower as the radius increase.
In the end, I will select a few different radii, plug in various normal forces and solve for μs. Then, I'll have a nice collection of curves.
So, I could use some help with creating the integral to solve for the total torque. My initial stab at it is
sum of the moments = 0
[tex] T - T_f = 0 [/tex]
[tex] T_f = ∫^r_0 μ_s*N*dx [/tex]
[tex] T_f = μ_s*N*∫^r_0 dx [/tex]
but this is merely x = r. I'm not confident this is correct.
Hmm, does the Normal force, N, depend on x and change as it moves further away from the center even though it's a completely rigid body? Yeah, I'm just not sure.