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Consider the frame of reference Ax'y'z' in translation with respect to the newtonian frame of reference Oxyz. We define the angular momentum
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Vector Mechanics For Engineers
- 2. Angular momentum conservation D h v' G h' A ball with mass m hits a racket with mass m, at a speed of v, and is then bounded back at a speed of v'. If the momentum of inertia of the racket about the center of mass G is I, find the angular speed of the racket about G after the hit.arrow_forwardA rigid bar AC revolves about A at constant speed of 1.2 rad/s. The slider moving on the rigid bar is allowed to follow spiral path defined by Ө r = 4.25 + - cm where 0 is the angle rotated by link AC with respect to π x-axis in radians. The magnitude of Coriolis acceleration of the slider when r = 6 cm, is cm/s². A Ө C Spiral path of point B Xarrow_forward1. Two mobile containers, A and B, carries raw materials for concrete batching plant. The containers' motions are defined by their velocity vectors: for container A, A = 6i + 4k (km/hr) and for container B, B = -4i +7k (km/hr). What is the angle between the line of action (path) of both containers? Express your answer in units of degree. 2. Two cables A and B are attached to a hook. Cable A exerts a pull with a magnitude and direction defined by the vector A = 6i + 4k (kN). Cable B is also attached to the same hook where cable A is attached, cable B exerts a pull with a magnitude and direction defined by the equation B = -4i +7k (kN). What should be the magnitude of pull exerted at cable B such that the line of action of resultant force is along the positive z-direction (the resultant lies along the positive z-axis)? Express your answer in unit of kN.arrow_forward
- Object #1 of mass 1.41 interacts with object #2 of mass 7.27. These objects interact only with each other and not with any other objects. At time t=9.45 the magnitude of the acceleration of object #1 is 8.30. What is the magnitude of the acceleration of object #2 at time t=9.45? All quantities are given in SI units and the answer should be given as a positive or negative number in Sl units. Only type a number into the answer box, do not type in units.arrow_forwardA vector v is given as function of time t by v = ti+t²j+tkm/s, where (i, j, k ) are unit vectors whose directions are fixed in the frame H. The angular velocity of H in frame Ris wH/R = ti +t2j +t³k rad/s. Find the magnitude of the derivative of v in frame R, that is Ri, at t = 1.67 s.arrow_forward4. A symmetric body moves without the influence of forces or torques. Let X3 be the symmetric axis of the body and the angular momentum L be along x;. The angle between the angular velocity and x, is a. Let ö and L initially be in the x, - x, plane. What is the angular velocity of the symmetric axis about L in terms I1, 13, a, and a ?arrow_forward
- Q2.A warplane turns left at an orbit with a radius of R = 500 m at a speed of 1600 km /h parallel to the ground. The angular velocity vector of the turbine rotor is in the negative direction (in front of the plane) with the speed 90000 rpm. The distance between the bearings of the rotor is 1.2 m and the total moment of inertia of the rotor is 220 kg.m? ( the rotor is acceppted as a disc and it is located in the middle of the bearings). The total forces (weight of the rotor + gyroscopic impact forces) acting on the front and rear bearings of the rotor during this rotational motion of the aircraft shall be determined. The total mass of the rotor is m = 1800 kg.arrow_forwardA shaft is rotating at a uniform speed with four masses m1, m2, m3 and m4 of magnitudes 300 kg, 450kg, 360kg and 390 kg respectively. The masses are rotating in the same plane. The corresponding radii of rotation are 200mm, 150mm, 250mm and 300mm. The angles made by these masses with respect to horizontal are 0°, 45°, 120° and 255° respectively. 1) Check the magnitude and position of balance mass if it radius of rotation is 200mm, and 2) Evaluate the effect of adding the balance mass to the system. solve it using garphical methodarrow_forward4. A weight, attached to a cord, is travelling on a smooth circular table. A cord is pulling the weight radially inward with a constant velocity of 5 cm/s. There are no forces in the 8-direction, so a = 0. 0 = 10 rad/s r=20cm 5 cm/s a. At the time shown on the figure, what is the radial component of acceleration? b. What is the angular acceleration, ö, of the block? (Hint: a = 0, but 0 +0)arrow_forward
- Five masses A, B, C , D and E are attached to a shaft and revolve in the different planes . The masses(B,C and D) are 60 kg, 50 kg, 70 kg . Their radius of rotations are 0. 5m. The angular position of the masses (B, C and D) are 600 , 900 and 2100 from mass A. Planes B,C,D and E 60cm ,120cm,200 cm,225cm from mass A Find the magnitude and position of the balancing mass for (A and E) ?arrow_forward1) Near the end of its takeoff roll, the airplane is "rotating" (nose pitching up) just prior to liftoff. The velocity and acceleration of the aircraft, expressed in terms of the motion of the wheel assembly C, are Vc and ac, both directed horizontally forward. The pitch angle is 0, and the pitch rate w = ė is increasing at the rate a = w . If a person A is walking forward in the center aisle with velocity L and acceleration L , both measured forward relative to the cabin, calculate the components of the position, velocity and acceleration vectors in the inertial frame shown as OXY (ground-fixed). Y Y Xc Xc Origin of the Bxy frame is at the point B, and the point C of this frame has a position Xc, velocity Vc, and acceleration ac with respect to the inertial frame OXY. L W = 0 (DEGREE/S) . (DEGREE/S²) XC Vc ac L a = ) (m) (km/h) (m/s²) (m) (m) | (m/s) . (m/s²) (DEGREE) 3,6 16 1660 235 22 20 10 3arrow_forwardOne morning, Connie walks from her house to go to a store that is 500 ft, S 40o W from her house. She starts walking 120 ft, SW; then continues walking 100 ft, 10o S of E; then sees a friend who is 700 ft, 30o N of E from where she is. What is her friend’s location, (magnitude and direction) relative to her house? (Answer: 667.54 ft, 21.79o N of E)arrow_forward
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