I am posed the following problem: My work so far is this: For part 1, we solve a system of equations: F_net = M*a = T - F_fr with F_fr the force of friction, Torque_net = I*alpha = T*r + F_fr*R since the torques from the tension and friction operate in the same direction, and a = alpha*R. First we find I = (1/2)(M)(R^2 + r^2). Then we substitute a/R = alpha. To get F_fr in terms of T, R, and r, I substituted the moment of inertia and the expression for alpha into the net torque equation. Solving that for M*a, I then substituted into the net force equation and solved for F_fr, which, after some algebra, ends in the glorious result: F_fr = T(R - r) / (R + r). The second part of the question is quite intriguing. Suppose that a > T/M. Then M*a > T, but M*a = T - F_fr. This implies that F_fr < 0, which has bizarre implications: the first is that r > R in the formula above, and the second (even more stunning) is that friction is actually pointing in the same direction as the relative motion! Is this supposed to happen? If so, can someone point me to an explanation of how this defies a supposed tenet of friction (friction opposes relative motion)? Did I make a mistake in setting up the system? Thanks for any help!