1. Mass moment of inertia The assembly is made of the slender rods that have a mass per unit length of 3 kg/m. Determine the mass moment of inertia of the assembly about an axis perpendicular to the page and passing through point O. 2. Kinetics: Force and torque. Equation of motion The 4-kg slender rod is initially supported horizontally by a spring at B and pin at A. Determine the angular acceleration of the rod and the acceleration of the rod's mass center at the instant the 100-N force is applied. 3. Work and energy: Use principle of work and energy The 10-kg uniform slender rod is suspended at rest when the force of F = 150 N is applied to its end. Determine the angular velocity of the rod when it has rotated 90 clockwise from the position shown. The force is always perpendicular to the rod. 3 m 0.4 m 0.8 m 0.4 m- 100 N 1.5 m 1.5 m B k-20 N/m 4. Conservation of Angular Momentum The 80-kg man is holding two dumbbells while standing on a turntable of negligible mass, which turns freely about a vertical axis. When his arms are fully extended, the turn- table is rotating with an angular velocity of 0.5 rev/s. Determine the angular velocity of the man when he retracts his arms to the position shown. When his arms are fully extended, approximate each arm as a uniform 6-kg rod having a length of 650 mm, and his body as a 68-kg solid cylinder of 400-mm diameter. With his arms in the retracted position, assume the man as an 80-kg solid cylinder of 450-mm diameter. Each dumbbell consists of two 5-kg spheres of negligible size. 0.20 m 0.65 m 0.3 m 0.3 m