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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/s 2, determine the magnitude of the velocity and acceleration of points A and B 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 acceleration of the wheel at this instant. Equations of Motion 3. Determine the acceleration of the block down the plane when it is released. The block has a mass m, and the cylinder has a mass M and a radius R. Assume the cylinder does not slip as it rolls, and the block slides on a smooth surface. The peg at B is smooth. MAE-2102 1 Summer 2004 Dynamics: Practice #2 Kinematics & Kinetics of Rigid Bodies Principal of Work and Energy 4. 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=(0.06θ2 + 7.5) N*m, where θ is in radians, determine the speed of the elevator when it has ascended 12 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. Conservation of Energy 5. 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 Impulse and Momentum 6. Gear A has a mass of 60 kg and a radius of gyration k C=160mm. Gear B has a mass of 25 kg and a radius of gyration k D =125 mm. 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 B in 3 s. Initially, gear A is rotating at ω1=2 rad/s. MAE-2102 2 Summer 2004 Dynamics: Practice #2 Kinematics & Kinetics of Rigid Bodies Conservation of Momentum 7. (19-42) A thin rod of mass m has an angular velocity ω0 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. Solve the problem (a) using the parameters given, (b) setting m=2 kg, ω0=4 rad/s, l=1.5 m. Extra Credit Instantaneous Center of Rotation Moment of Inertia MAE-2102 3 Summer 2004