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The rigid body (slab) has a mass m and rotates with an angular velocity ω about an axis passing through the fixed point O Show that the momenta of all the particles composing the body can be represented by a single
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- A ring of mass m =1 kg and radius R = 1m is attached to a vertical shaft by means of a frictionless pin. Coordinates xyz are fixed to the ring as shown and the frictionless pin at A is aligned with the x-axis. The vertical shaft precesses about the Z-axis with constant angular velocity 2 = 1 rad/s. (a) At a particular moment when 0 = 30° and = 4 rad/s, find the value of Ö . This comes from a sum of the moments about the x-axis. Do not neglect gravity. (b) Find the torque or moment necessary that must be applied about the vertical shaft in order to keep it turning at a constant rate of N = 1 rad/s. Ring R XG A 1 Ixx = lyy =mR? G Iz = mR?arrow_forwardThe 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, arearrow_forward(dynamic)arrow_forward
- Determine the equivalent of the system using the angular motion of the bararrow_forwardA rotating shaft carries four unbalanced masses 20 kg, 16 kg, 18 kg and 14 kg at radii 55 mm, 65 mm, 75 mm and 65 mm respectively. The 2nd, 3rd and 4th masses revolve in planes 80 mm, 160 mm and 280 mm respectively measured from the plane of the first mass and are angularly located at 65°, 135° and 270° respectively measured clockwise from the first mass.The shaft is dynamically balanced by two masses, both located at 55 mm radii and revolving in planes mid-way between those of 1st and 2nd masses and midway between those of 3rd and 4th masses. Determine, balancing mass by drawing couple polygon and their respective angular position graphically.arrow_forwarda rotating shaft carries four unbalanced masses 18 kg, 14 kg, 16 kg and 12 kg at radii 50 mm, 60 mm, 70 mm and 60 mm respectively. the 2nd, 3rd and 4th masses revolve in planes 80 mm, 160 mm and 280 mm respectively measured from the plane of the first mass and are angularly located at 60°, 135° and 270° respectively measured clockwise from the first mass looking from this mass end of the shaft. the shaft is dynamically balanced by two masses, both located at 50 mm radii and revolving in planes mid-way between those of 1st and 2nd masses and midway between those of 3rd and 4th masses. determine, graphically or otherwise, the magnitudes of the masses and their respective angular positions.arrow_forward
- 6. Multiple forces are acting on the 3.00 kg uniform beam below. Find the magnitude and direction of the angular acceleration of the beam about the axis of rotation at C. * 25 N 1 30° 20° 45° 2.0 m C 10 N 4.0 m 30 Narrow_forwardFor the circular thin plate with a square hole as shown in the image below, its radius R = 0.48 m and the side of the square /= 0.21 m, and the material has a mass per unit area of 12 kg/m2. If at the instant shown, it is subjected to a force P = 38 N, and has a counterclockwise angular velocity of W = 2.6 rad/s, determine magnitude of the support reaction at point O at this instant. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper unit. Take g = 9.81 m/s?. R Parrow_forwardA shaft carries four masses A,B,C and D of magnitude 220 kg, 320 kg, 420 kg and 220 kg respectively and revolving at radii 9cm, 7cm, 6 cm and 8cm in planes measured from A at 30cm, 45cm and 60cm. The angles between the cranks measured from A anticlockwise are 45°, 90° and 130°. The balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 20cm, between X and Y is 50cm. If the balancing masses revolve at a radius of 15cm, find their magnitudes and angular positions.arrow_forward
- The bar AB is uniform and has a mass of 50.0 kg. At the moment shown, the rod has an angular velocity of 4.00 rad/s and spring is stretched by 0.30 m. The force constant of the spring is 25.0 N/m.a) Determine whether or not the bar will reach the horizontal position.b) If the bar becomes horizontal, calculate its angular velocity at that position. If not, calculate the angle the bar makes with the horizontal when it comes to rest momentarily.arrow_forwardHW2 A uniform disc of 80 mm radius has a mass of 2000 g. It is mounted centrally in bearings that maintain its axle horizontally. The disc spins about its axle with a constant speed of 550 r.p.m. while the axle precesses uniformly about the vertical at 50 r.p.m. The directions of rotation are shown in the figure below. If the distance between the bearings is 130 mm, find the resultant reaction at each bearing due to the mass and gyroscopic effects. Ho +X +y * -yarrow_forwardONLY HANDWRITTEN pleasearrow_forward
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