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The 400-mm bar AB is made to rotate at the rate
Fig. P15.234 and P15.235
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Vector Mechanics For Engineers
- An engine flywheel has a mass of 120 kg and a radius of gyration of 630 mm. At an instant when the flywheel runs at 600 rev/min, an acceleration torque of 150 Nm was applied for a period of 10 seconds. Determine the: (i) final speed of the flywheel in rev/min. (ii) number of flywheel revolutions made during the acceleration period. (iii) kinetic energy of rotation of the flywheel.arrow_forwardAt the instant shown, the 200-lb bar rotates clockwise at 4 rad/s. The spring attached to its endalways remains vertical due to the roller guide at C. If the spring has an unstretched length of 2ft and a stiffness of k = 9 lb/ft, determine the angular velocity of the bar the instant it has rotated 39° clockwise.arrow_forwardThe wheel is spinning about shaft ABAB with an angular velocity of ωs=10rad/sωs=10rad/s, which is increasing at a constant rate of ω˙2=6rad/s2ω˙2=6rad/s2, while the frame precesses about the zzz axis with an angular velocity of ωp=12rad/sωp=12rad/s, which is increasing at a constant rate of ω˙p=3rad/s2ω˙p=3rad/s2. Determine the velocity of point CC located on the rim of the wheel at this instant. Determine the acceleration of point CC located on the rim of the wheel at this instant.arrow_forward
- A drum of radius r1 = 3 in. is mounted on a cylinder of radius r2 = 6 in. A cord is wound around the drum, and its extremity D is pulled to the left with a constant velocity of 6 in./s, causing the cylinder to roll without sliding. Determine: 1. The angular velocity of the cylinder. 2. The velocity of the center of the cylinder A. Select one: A. ω=6 rad/s; and VA = 30 in/s. B. ω=4 rad/s; and VA = 16 in/s. C. ω=5 rad/s; and VA = 25 in/s. D. ω=2 rad/s; and VA = 6 in/s.arrow_forwardInside a machine, two gears, A and B, HINGED at their centers, are meshed with each other such that gear A transmits torque and speed to gear B. Gear A has a mass mA=2 kg, radius rA=175 mm, and radius of gyration kA=150 mm. Gear B has a mass B=5 kg, radius rB=525 mm, and radius of gyration kB=400 mm. From rest, a counter-clockwise couple M of constant magnitude 6 Nm is applied to Gear A. Which of the following is closest to the magnitude of the angular acceleration of gear B, in radians per square seconds (rad/s2)?3.0044.814.9445.6arrow_forwardGears A and B each have a mass of 2.4 kg and a radius of gyration of 60 mm, while gear C has a mass of 12 kg and a radius of gyration of 150 mm. A torque M with constant magnitude of 10 N.m to gear C. Determine a) the number of revolutions of gear C that is required for its angular velocity to increase from 100 to 450 rpm. b) the corresponding tangential force acting on gear A Please include the free body diagram if necessary.arrow_forward
- The turbine rotor of a ship has a mass of 2.2 tonnes and CO1(L2) rotates at 1800 rpm clockwise when viewed from the aft The radius of gyration of the rotor is 320 mm. Determine the gyroscopic couple and its effect when (a) The ship turns right at a radius of 250 m with a speed of 25 km/h. (b) The ship pitches with the bow rising at an angular velocity of 0.8 rad/s (c) The ship rolls at an angular velocity of 0.1 rad/s.arrow_forwardAn aeroplane makes a complete half circle of 70 metres radius, towards left, when flying at 500 km per hr. The rotary engine and the propeller of the plane has a mass of 600 kg and a radius of gyration of 0.3 m. The engine rotates at 2500 r.p.m. clockwise when viewed from the rear. Find the gyroscopic couple on the aircraft.arrow_forwardThe rod AB has a mass of 20 kg,the mass of the piston A and B are both 5kg. Piston B is attached to a spring of constant k = 1200 N/m. The spring is un-stretched when θ = 0. If the rod is released from rest whenθ = 45° Please find÷ (1) the moment inertia of the rod AB about its mass center G (2)The angular velocity of rod AB at θ = 0° (3)the velocity of piston A at θ = 0° (4) the velocity of Piston B at θ = 0° (hint: regard the piston A, B, rod as a system, during the motion, except the spring, the weight of rod AB, the weight of pistonB also does work). g = 9.8 m/s2arrow_forward
- A stepped cylinder has the dimensions R₁ = 0.30 m, R₂ = 0.65 m, and the radius of gyration, k, is 0.35 m. The mass of the stepped cylinder is 100 kg. Weights A and B are connected to the cylinder. If weight B has a mass of 80 kg, and weight A has a mass of 50 kg, how far does A move in 5 seconds? In which direction does it move? (Draw all FBDs)arrow_forwardFind the magnitude and position of the balancing mass at a radius of 13cm by using the analytical method. Three masses m1, m2, m3, are attached to a shaft and revolve in the same plane. The masses are 12kg, 10kg, and 15kg respectively and their radii of rotations are 5cm, 6cm, 7cm respectively. The angular position of the masses m2, m3 are 45° and 145° from the mass m1.arrow_forwardRing C moves downwards at 2 m/s. Determine the value of point B velocity (vB =?), Angular velocity of the arm CB (wBC) and the position vector B in relation to C rB/C for the situation shown in the figure.arrow_forward
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