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Engineering Mechanics II Practice Exam #2 Planar Constant Angular Acceleration & Dependent Motion 1. Wheel B has radius RB = 20 cm and is initially rotating at 20 RPM while undergoing a constant angular acceleration of =10 rad/s2 in the same direction. How fast is it rotating at the end of the 5 seconds? How many revolutions does it make in the 5 seconds? Point P is on wheel B at a distance of 15 cm from the center. What is the total acceleration vector of point P at the end of 5 seconds? Wheel A , which has radius R A=10 cm, contacts wheel B at point C with no slipping. What is the initial angular speed of wheel A? Conservation of Energy 2. At the instant shown, the 50-lb bar is rotating downwards at 2 rad/s. The spring attached to its end always remains vertical due to the roller guide at C. If the spring has an unstretched length of 2 ft and a stiffness of k=6 lb/ft, determine the angular velocity of the bar the instant it has rotated downward 30 degrees below the horizontal. Principal of Work and Energy 3. The elevator car E has a mass of 1.80 Mg and the counterweight C has a mass of 2.30 Mg. If a motor turns the driving sheave A with a torque of M=15 N*m, where is in radians, determine the speed of the elevator when it has ascended 14 m starting from rest. Each sheave A and B has a mass of 150 kg and a radius of gyration of k=0.2 m about its mass center or pinned axis. Neglect the mass of the cable and assume the cable does not slip on the sheaves. MAE-2104 1 Ver. B, Rev 2 Engineering Mechanics II Practice Exam #2 Planar Rotating Reference Frames 4. Arm AB has length RAB =0.12 meter. It is rotating clockwise at a constant rate of A=2 rad/s and is horizontal at the instant shown. Arm BC has length RBC = 0.1 meter. It is rotating clockwise at a constant rate of B=3 rad/s and is vertical at the instant shown. Collar C has a speed measured relative to arm BC of 4 m/s downward along arm BC, and is accelerating at 5 m/s2 downward, also measured relative to BC. Find the inertial velocity and acceleration of collar C at this instant. (Assume total=5 rad/s and total=0 rad/s2 Planar Kinetics: Fixed-Point Rotation 5. The pendulum shown is comprised of a rod of length 3 feet with a mass of 0.5 slugs and a disk of radius 0.75 feet and a mass of 0.25 slugs affixed to the end of the rod. The other end of the rod is fixed on a vertical wall at point O, and at the instant shown is horizontal and rotating downward at =8 radians/sec. Find the center of mass of the pendulum. How fast is the center of mass moving? Find the tangential and normal acceleration components of the center of mass. Find the moment of inertia of the pendulum about point O. Planar Kinetics: Newton’s Law 6. Determine the acceleration of the center of mass of the cylinder at the instant shown. The tension in the rope is 12 N. The cylinder has a mass of 4 kg, and a radius of 0.02 m. Assume the cylinder does not slip as it rolls. MAE-2104 2 Ver. B, Rev 2