I have searched high and low on the internet for the correct equation to determine the angular velocity of a rigid body under the following circumstances, and have not been able to find one. Could someone show me the correct equation? Suppose a long thin rigid rod lies on the surface of a cart, which initially is at rest. One end of the rod can rotate freely around a vertical axis attached to the cart. A small object prevents the rod from rotating clockwise. The cart can move parallel to the y-axis of an x-y coordinate system. The rod initially lies 45 degrees with respect to the x-axis. At some point in time we push the cart, giving the cart and rod an initial velocity equal to v. At a later point in time the cart makes an inelastic collision with a front bumper. Immediately, the rod rotates in the counter-clock wise direction. I need to know what the angular velocity of the rod is after the collision. We denote the mass of the rod as m, the mass of the cart as M, the initial angle of the rod as theta, the length of the rod as l, and the moment of inertia of the rod as: I = 1/3 m l sq I know we CANNOT use the below equation to determine the final angular velocity rod: L = m v r cos theta because this equation applies to point particles, but the rod is a solid, rigid body. (Assume for the sake of symmetry, there is an equal small hole at the other end of the rod so that the center of mass of the rod is at its geometric center.) I have no idea what the correct equation is. Could someone please show me and also a general equation that applies for any shape of a rigid body.