A cylinder of length l, radius r, and mass m is constrained to rotate with constant angular velocity ? about an axis passing through the center O of the cylinder and making an angle a with the long axis of the cyclinder.
(a) Evaluate all elements of the moment of inertia tensor I ^ for a body frame where one axis is along the axis of the cylinder. You have to show explicity how you compute each matrix element of I ^.
(b) Find an expression for the angular momentum vector L about O.
(c ) Find an expression for the kinetic energy of the cylinder.
(d) Use the Euler equations to find an expression for the torque vector N.