1. The problem statement, all variables and given/known data A uniform cylinder of mass M and radius R can be rotated about a perpendicular axle through its centre. A particle of mass m is attached to the cylinder's rim. The system is rotated with angular velocity w about the axle, which is held in a fixed direction during the motion. Discuss the angular momentum L of the system about the centre of the cylinder. Find the angle between w and L, and explain why torque must be applied to maintain the axle's direction. 2. Relevant equations L = Iw L = r x p = r x mv = rmv sin(theta) v = wxR 3. The attempt at a solution After drawing a diagram, I am aware that there must be a torque to counteract the gravitational force of the point mass on the cylinder. Hence, I am suspecting the angle between w and L to be non-zero. I know that if we assume that the cylinder is rotating counter-clockwise when viewed from upwards (above the plane of the cylinder) then the w vector is directed upward along the axis around which it rotates. My thoughts are that we can simply take the vector sum of angular momentum contributions from the point mass and the cylinder as this is appropriate for rigid bodies and particles. Where I am stuck is developing a formula for the angular momentum of the cylinder. The direction of the velocity of the cylinder while rotating is what is really getting me. I keep imagine it as being perpendicular to the axis through the centre of the cylinder (i.e. tangential to the circular path that the cylinder rotates in). In which case, there is a moment arm of l/2 where l is the length of the cylinder and some velocity v, which could be rewritten as v = wxR in which case the moment of inertia of the cylinder would be (l/2)xM(wxR). However I am almost uncertain that I am not doing that right. In terms of the point mass, I intended to (as previously mentioned) summate it vectorially with the angular momentum of the cylinder to determine the angle between w and L. The angular momentum of the point mass about the axis would simply be (l/2)xmv.