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MAE-2102 Key Problems Unit #2 Kinematics & Kinetics of Rigid Bodies Chapter 16 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 points A and B on the blade after the blade has rotated through two revolutions. Chapter 16 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. Chapter 17 3. Determine the acceleration of the block down the plane when it is released. The block has a mass of 2 kg and the cylinder has a mass of 5 kg and a radius of 0.05 m. Let θ=30o and φ=30o. Assume the cylinder does not slip as it rolls and the block slides on a smooth surface. The peg at B is smooth. Chapter 18 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 1 Ver. A, Rev. 1 MAE-2102 Key Problems Unit #2 Kinematics & Kinetics of Rigid Bodies Chapter 18 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=(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. Chapter 19 6. Gear A has a mass of 60 kg and a radius of gyration kC=160mm. Gear B has a mass of 25 kg and a radius of gyration kD =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. (Hint: The linear velocity of the point where both gears meet is a constant.) Chapter 19 7. 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. R. Gist 2 Ver. A, Rev. 1