21-23. Show that if the angular momentum of a body is determined with respect to an arbitrary point A, then H, can be expressed by Eq. 21–9. This requires substituting PA = PG + PG/A into Eq. 21-6 and expanding, noting that SPg dm = 0 by definition of the mass center and VG VA + co X PG| A- PGJA PG PA
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- Q-4) The rod, having a weight of 16N and a length of 2.5m, contains a joint at O which is 0.5m distant from point B. The other end of the rod is attached to a 2,5 m- 0,5 m spring that is compressed by 4cm A with Ks= 250N/cm. At this moment the rod is horizontal. When released; calculate it's angular velocity (passing by the vertical position) and reaction forces at the joint 0.The 23-kg uniform thin hollow square plate is pinned at point O, and its side L = 0.3 m. If it is subjected to the constant moment M = 82 N·m and is released from rest from the position as shown, determine its angular velocity W (in rad/s) when it has rotated 45 Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s². M Your Answer: AnswerThe rotor of a turbojet engine of an aircraft has a mass 180 kg and polar moment of intertia 10 kg.m2 about the rotor axis. The rotor rotates at a constant speed of 1100 rad/s in the clockwise direction when viewed from the front of the aircraft. The aircraft while flying at a speed of 800 km per hour takes a turn with a radius of 1.5 km to the left. The gyroscopic moment exerted by the rotor on the aircraft structure and the direction of motion of the nose when the aircraft turns, are
- The 21-kg uniform thin hollow square plate is pinned at point O, and its side L = 0.5 m. If it is subjected to the constant moment M = 78 N•m and is released from rest from the position as shown, determine its angular velocity w (in rad/s) when it has rotated 45°. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s2. `L MV Your Answer: AnswerThe 21-kg uniform thin hollow square plate is pinned at point O, and its side L = 0.5 m. If it is subjected to the constant moment M = 78 N·m and is released from rest from the position as shown, determine its angular velocity W (in rad/s) when it has rotated 45°. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s². L Your Answer: AnswerThe uniform disk is initially at rest and has a mass of 24 kg. Its moment of inertia about its mass center is given by I =mr². A 100 N (constant) force F acts upon it as shown and it rolls without slip on the horizontal surface. Find: a) The velocity of its mass center G after it has moved 1.8 m. b) Include a detailed free body diagram(s)! f-100 N
- *13=108. The collar, which has a weight of 3 lb, slides along the smooth rod lying in the horizontal plane and having the shape of a parabola r = 4/(1 – cos 0), where 0 is in radians and r is in feet. If the collar's angular rate is constant and equals ò = 4 rad/s, determine the tangential retarding force P needed to cause the motion and the normal force that the collar exerts on the rod at the instant 0 = 90°.W = O rad 8 h A 1.4 m by 1.4 m thin plate is used as target practice at a firing range where participants are shooting for sport. If the plate has a mass of mplate = 16 kg and is pinned at point O, determine the angular velocity of the plate just after a 5 g bullet, shot at a velocity of Ubullet = 480, is embedded in it. The bullet hits a vertical distance h = 1.05 m away from point O. m S (CC BY UBC EngineeringThe rolling motion of the circle with a zero mass is defined by a velocity V-1.2m.s at the Center of the disk. Calculate d=12m the ongulor Veldrity W. At the time Os is W=0. 163
- A helicopter is moving at an inertial speed of vo = 10 m/s while its rotor blades spin at w = 40 rad/s CCW. Consider a body frame B = {G, 6₁, 6₂, 6₂} that is located at the rotor hub and has ₁ axis aligned and rotating with one of the blades. The tip of another blade is located at position P with respect to the body frame, that is, rp/G = 3 b₁ + 3 b2 meters. 1. What is the inertial velocity Tvp/o of P with respect to O in frame I? Express your answer in terms of the unit vectors of frame I. Assume 0 = 15 deg. ხე. i3 22 i3 b1 i₁ 2. Now suppose that at the same instant as in Part A the rotor blade experiences a failure from a bird strike and a segment of the blade at P brakes off and is flung away from the helicopter at a body-relative speed Bvp/G = 20 6₂ m/s. What is the inertial velocity Tvp/o of P with respect to O in frame I? Express your answer in terms of the unit vectors of frame I. Bup/G b2 VO VOA drum with a radius of 0.5 ft has a weight of 90 lb and a radius of gyration ko = 0.3 ft. A weightless cable is wrapped around the drum and rotates it clockwise. If the cable is being pulled by a force P = 15 lb, determine the time needed to increase the drum's angular velocity from w1 = 6 rad/s to wz = 24 rad/s. 0.5 ft૨૩: If P = 200 N and the 15-kg uniform slender rod starts from rest at 0 = 0°, determine the rod's angular velocity at the instant just before 0 = 45°. Ans.: @₂ = 4.97 rad/s 45° 600 mm P = 200 N SOC