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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
- consider the slider-crank mechanism shown. Crank AB is 3.00 m long. Rod BD is 2.00 m long. The velocity at point B is 6.00 m/s, ↘45.0°. a. speed of the piston at D? b. On which area is the instantaneous center of rod AB located?arrow_forwardHW1 Four masses A, B, C and D are attached to a shaft and revolve in the same plane. The masses are 12 kg, 10 kg, 18 kg and 15 kg respectively and their radii of rotations are 40 mm, 50 mm, 60 mm and 30 mm. The angular position of the masses A, B, C and D are 60°, 90° and 70° from the mass A. Find the magnitude and position of the balancing mass at a radius of 100 mm.arrow_forward2. 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_forward
- A 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_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_forwardQ2.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_forward
- 4. 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_forwardFive 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_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_forward
- 4. 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_forwardA 1024-kg blue ball is dropped from an initial z-position of 5.4 x 106 m through the center of a planet with radius 6.3 x 106 m. If the mass of the planet is 37.7 x 1015 kg, measure the displacement of the ball at time t = 5 s?arrow_forwardi need the answer quicklyarrow_forward
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