ed to the mass of L 521 Consider the gyroscopic turn indicator in Problem 5.13 in a situation where the torque M is not present, so that ẞ is a variable angle. The precession rate 2 is a speci- fied function of time, and the spin rate w, is held constant by a servomotor. Let I denote the moment of inertia of the flywheel about axis AB, and let I, be the cen- troidal moment of inertia perpendicular to axis AB. Derive the differential equation of motion for ẞ in terms of Q and w₁. DC is nivated from the and of al precession rate is w Problem 5.13 Ω B $15 A 50-kg rectangular plate is mounted diagonally on a shaft whose mass is negligible. The system was initially at rest when a constant torque of 5 kN-m is applied to the shaft. Determine the reactions at bearings A and B four seconds after the applica- tion of the torque. 200 mm- -200 mm 150 mm 250 mm Problem 5.15 5 kN-m B an motion. The mass of the vertical system 5.42 Collars A and B are interconnected by a bar on which a 10-kg sphere of 100-mm rotates freely about the vertical axis. Initially, s=240 mm, and the collars are not diameter is mounted. The mass of the collars and the bar is negligible. The s 100 mm B 53.13° Ο ΣΩ A ΩΣ Problem 5.41 300 mm 120 mm A 120 mm B Problems 5.42 and 5.43 he sphere at that position? red for collar A to reach -180 mm? of the initial angular speed y the system in Problem 5.42 is at s-180 mm, at which position the rotation ption 300 mm in the subsequent motion. If so, what is the angular velocity of e about the vertical axis is 30 rev/min. Determine whether collar A attains the Amicircular plate is falling at speed v with its plane oriented horizontally. It strikes the edge at corner A, and the impact is perfectly elastic (ie., the recoil velocity of A is upward). The interval of the collision is Ar. Derive expressions for the velocity of the center of mass and the angular velocity at the instant following the on. Also, derive an expression for the collision force exerted between the plate and the ledge. celeration of The bar is by 100 mm. drontal at and ession lined ad/s Dent not Problem 5.44 steady precession about the vertical axis at angular speed 2 as it maintains the orien A slender bar of mass m, which is suspended by a cable from pivot A, executes a (a) Determine Q and the angle of inclination B. tation shown. (b) An impulsive force at end B, parallel to the initial velocity of that end, acts over a short time interval Ar. Determine the magnitude of F for which the angular velocity of the bar at the conclusion of the impulsive action is horizontal. What are the corresponding velocity of the center of mass G and the angular velocity of the bar? Problem 5.45 546 The flyball device consists of two 500-g spheres connected to the vertical shaft by a parallelogram linkage. This shaft, which passes through collar C supporting the link- age, rotates freely. The system is initially rotating steadily at 900 rev/min about the vertical axis, with 0-75°. A constant upward force F is applied to the vertical shaft, 5.46 The flyball device consists of two 500-g spheres connected to the vertical shaft by a parallelogram linkage. This shaft, which passes through collar C supporting the link- age, rotates freely. The system is initially rotating steadily at 900 rev/min about the vertical axis, with 0 = 75°. A constant upward force F is applied to the vertical shaft, 242 5/Newtonian Kinetics of a Rigid Body tude of F for which the system will reach 0 = 15°. The mass of the shaft and the bars causing point B to move upward and 0 to decrease. Determine the minimum magni- in the linkage is negligible. Ω 9 100 mm Problem 5.46 A 50 mm haut