A barrel is lowered into a boat using the illustrated apparatus. The barrel can be considered to be a uniform cylinder with M=100kg and r=0.40m. The weight on the other end of the rope has m=30kg. Assume that the barrel does not slip against the wall, that the other 2 pulleys are massless and frictionless and the rope does not stretch and has no mass. What is the linear acceleration of the mass m? Answers are in m/s^2.
The Attempt at a Solution
So basically I set the tension in the rope as T, and did an Fnet equation for the small block. From there I got Fnet = T-30(9.8) = 30a
So I isolated for T and got T=30(a+9.8)
From that I used T to find the torque that it exerted on the cylinder. Now this is where I run into the problem, I know torque = T x R, but do I treat the point of contact between the cylinder and the wall as the pivot point, so R=0.8, or do I treat the center of the cylinder as the pivot point, so R=0.4?
Also, can the center of gravity of the cylinder itself produce rotational torque about the point of contact between the wall and the cylinder (i.e. torque = mgr)?