1. The problem statement, all variables and given/known data A cylinder of radius R, length h, and mass m2 has two ends of mass m1 and radius R. Inside the cylinder is liquid which can be modelled as a solid cylinder of mass M, radius R and length h. This cylinder is placed onto a routegh surfaced conveyer belt which is stationary. When switched on, the belt has acceleration f. The time from which the cylinder starts to move is t, \theta is the angle through which the cylinder rotates and x is the distance moved by the centre of mass of the cylinder due to the rotation \theta. 2. Relevant equations Rolling condition = R\theata = x I = Moment of inertia = 1/2MR^2 second law:F = ma (where m is the total mass of the system) m = (M + 2m1 + m2) v = dx/dt w = -d^2x/dt^2 a = f + w a) Use the rolling condition to show that the acceleration of COM of the cylinder is (f - Rw). b) Draw a force diagram, express forces in equation form. c) Appliy newtons second law, show the equation of motion of the COM of the cylinder d) Find the torque relative to the COM associated with each force identified in part b. e) Show that the moment of inertia is (1/2M +m1 + m2)R^2 3. The attempt at a solution a) When the can rolls anticlockwise, the distance rolled is x, therfore R\theta = x. Relative to the origin, the position vector of the COM is Rj - xi, therfore the velocity is -dx/dt (since R is constant), therefore the acceleration is -d^2x/dt^2 = w. Therefore, the total acceleration of the COM is f - Rw as given in the question. b) Should there be 3 forces? W, N (normal reaction) and F (force due to the conveyor belt moving)? c) F = ma = (M + 2m1 +m2)(f + w) d) Not attempted this one yet (but any assistance appreciated)! e) I = 1/2mR^2 = 1/2(M + 2m1 + m2)R^2 = (1/2M + m1 + 1/2m2)R^2. Uhm... why is this wrong? Any hints/tips/help appreciated.