Hinged beam falls without slipping: find the final angular velocity of the rod and speed at the tip.

00:00 In this rigid body energy conservation problem, a hinged beam falls without slipping and the main goals are to find the final angular velocity of the rod and the speed at the tip when the rod hits the ground. 00:24 Potential energy of the beam: this is an energy conservation problem, and we start with a reminder of how to calculate the potential energy of a rigid body: Mgy_cm. So we need to find the initial height of the center of mass of the beam. Since the beam is uniform, the center of mass occurs at the geometric center, and we apply trigonometry to compute the initial height of the center of mass. 01:19 Apply conservation of energy to the rigid body: now we apply conservation of energy, E_i=E_f. The initial energy is entirely gravitational potential energy, and the final energy is entirely rotational kinetic energy. We set up the energy conservation equation Mgy_cm=1/2*I(omega)^2. Plugging in the formula for the moment of inertia of a rod rotated about one end, we are left with an equation in which omega is the only unknown, and we solve for the final angular velocity of the beam when it hits the ground. 02:42 Find the speed at the tip of the rod: this is the easy part - simply apply the relation v=r*omega and we've got the tangential speed at the tip of the beam when it hits the ground.