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Dynamics: Practice #2 Kinematics & Kinetics of Rigid Bodies Show all work for partial credit. Use additional paper if necessary. Kinematic Equations 1. The vertical-axis windmill consists of two blades that have a parabolic shape. If the blades are originally at rest and begin to turn with a constant angular acceleration of αe = 0.5 rad/s2, determine the magnitude of the velocity and acceleration of point A on the blade after the blade has rotated through two revolutions. Velocity and Acceleration Vectors 2. At a given instant, the slider block B is traveling to the right with the velocity and acceleration shown. Determine the angular velocity and acceleration of the wheel at this instant. The radius of the wheel is 5 inches. Equations of Motion 3. Determine the acceleration of the cylinder. 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. Conservation of Energy 4. 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. R. Gist (Sum. ’06) 1 of 2 Ver. B, Rev. 1 Dynamics: Practice #2 Kinematics & Kinetics of Rigid Bodies Principal of Work and Energy 5. 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 θ 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. Principal of Impulse and Momentum 6. Gear A has a mass of 60 kg and a radius of gyration kC=160mm. If a motor supplies a torque having a magnitude M=(1.2t) N*m, where t is in seconds, to gear A, determine the angular velocity of gear A in 3 s. Initially, gear A is rotating at ω1=2 rad/s. Conservation of Momentum 7. A thin rod of mass 2kg and length l=1.5 m has an angular velocity ω0 = 4 rad/s while rotating on a smooth surface. Determine its new angular velocity just after its end strikes and hooks onto the peg and the rod starts to rotate about P without rebounding. R. Gist (Sum. ’06) 2 of 2 Ver. B, Rev. 1