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A half-cylinder with mass m and radius r is released from rest in the position shown. Knowing that the half-cylinder rolls without sliding, determine (a) its angular velocity after it has rolled through 900, (b) the reaction at the horizontal surface at the same instant. (Hint: Note that
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Vector Mechanics For Engineers
- A disk with mass m and radius R is released from rest at a height h and rolls without slipping down a ramp. What is the velocity of the center of the disk when it reaches the bottom of the slope? (Hint Use the work-energy principle. At each instant the disk rotates around the contact point C, thus the inertia used for rotatonal kinetic energy should be computed around point C not point G.) m C harrow_forwardThe 30-kg turbine disk has a centroidal radius of gyration of 175 mm and is rotating clockwise at a constant rate of 60 rpm when a small blade of weight 0.5 N at point A becomes loose and is thrown off. Neglecting friction, determine the change in the angular velocity of the turbine disk after it has rotated through (a ) 90°, (b ) 270°.arrow_forwardConsider a rigid body initially at rest and subjected to an impulsive force F contained in the plane of the body. We define the center of percussion P as the point of intersection of the line of action of F with the perpendicular drawn from G(a) Show that the instantaneous center of rotation C of the body is located on line GP at a distance GC = k2/GP on the opposite side of G. (b) Show that if the center of percussion were located at C, the instantaneous center of rotation would be located at P.arrow_forward
- Two disks each have a mass of 5 kg and a radius of 300 mm. They spin as shown at the rate of w1 = 1200 rpm about a rod AB of negligible mass that rotates about the horizontal z axis at the rate of w2. Determine the maximum allowed value of w2 if the magnitudes of the dynamic reactions at points C and D are not to exceed 350 N each.arrow_forwardThe 10-oz disk shown spins at the rate w1 = 750 rpm, while axle AB rotates as shown with an angular velocity w2. Determine the maximum allowable magnitude of w2 if the dynamic reactions at A and B are not to exceed 0.25 lb each.arrow_forwardA slender rod of length l and weight W is pivoted at one end as shown. It is released from rest in a horizontal position and swings freely. (a ) Determine the angular velocity of the rod as it passes through a vertical position and determine the corresponding reaction at the pivot. (b ) Solve part a for W = 1.8 lb and l = 3 ft.arrow_forward
- Disk A has a mass mA = 3.5 kg, a radius rA = 255 mm, and an initial angular velocity wOA = 300 rpm clockwise. Disk B has a mass mB = 1.8 kg, a radius rB = 150 mm, and is at rest when it comes into contact with disk A. Knowing that µk : 0.33 between the disks and neglecting rolling friction, determine the moment of reaction on the support at C, in N-m. = 00 B A C TA TBarrow_forwardA collar with a mass of 1 kg is rigidly attached to a slender rod AB of mass 3 kg and length L = 600 mm. The rod is released from rest in the position shown. Determine the distance d for which the angular velocity of the rod is maximum after it has rotated through 90°.arrow_forwardA 5.32-kg disk A of radius 0.445 m initially rotating counter-clockwise at 436 rev/min is engaged with a 6.72-kg disk B of radius 0.275 m initially rotating clockwise at 528 rev/min, where the moment of inertia of a disk is given as I = ½ mi?. Determine their combined angular speed (in rpm) and direction of rotation after the meshing of the two disks. Remember to show clearly the equations that you use!!'arrow_forward
- The space capsule has no angular velocity when the jet at A is activated for 1 s in a direction parallel to the axis. Knowing that the capsule has a mass of 1000 kg, that its radii of gyration are Kz=Ky =1.00m and Kz=1.25m A produces a thrust of 50 N, determine the axis of precession and the rates of precession and spin after the jet has stopped.arrow_forwardProblem (1) Gears A and B each have a mass of 4 kg and a radius of gyration of 75 mm about their centers, while gear C has a mass of 15 kg and a radius of gyration of 180 mm about its center. A couple moment M = (0.20) N-m is applied to gear C. Determine the number of revolutions gears A and B experience if gear C increases its angular velocity from 25 rpm to 500 rpm. B 80 mm S0 mm 200 mmarrow_forward4. Each of the gears A and B has 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 couple M of constant magnitude 10 Nm is applied to gear C. Determine (a) the number of revolutions of gear C required for its angular velocity to increase from 100 to 450 rpm, (b) the corresponding tangential force acting on gear A. В S0 mm, S0 mm 200 mm. Marrow_forward
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