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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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Engineering Mechanics
- A 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_forward3.32). As shown in Figure 3, a yo-yo toy is formed by wrapping a massless cord around adisk of radius R= 0.2 m and mass M=3 kg. The cord is vertical and its top end is fixed and the disk isinitially stationary. The cord remains vertical for the entire motion and does not slide on the disk.When the disk is released from rest, it falls down by a distance H=0.8 m, The moment of inertia ofthe disk around its center is I disk=1/2mdiskR^2a . Find the angular acceleration of the disk when it is lowered by a distance H.b . Find the angular velocity of the disk when it is lowered by a distance H.arrow_forwardThe connecting rod of a horizontal reciprocating engine is 400 mm and length of the stroke is 200mm. The mass of the reciprocating parts is 125 kg and that the connecting rod is 100 kg. The radius of gyration of the connecting rod about an axis through the centre of gravity is 120 mm and the distance of centre of gravity of the connecting rod from big end centre is 160 mm. The engine runs at750 r.p.m. Determine graphically the torque exerted on the crankshaft when the crank has turned 30° from the inner dead centre.arrow_forward
- The uniform 140-lblb beam is initially at rest when the forces are applied to the cables. Set FAFAF_A = 70 lblb and FBFBF_B = 190 lblb .(Figure 1) Determine the magnitude of the acceleration of the mass center at this instant. Determine the angular acceleration of the beam at this instant.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_forwardGears A and B each have a mass of 2.4 kg and a radius of gyration of 60 mm, while gear C has a mass of 12 kg and a radius of gyration of 150 mm. A torque M with constant magnitude of 10 N.m to gear C. Determine a) the number of revolutions of gear C that is required for its angular velocity to increase from 100 to 450 rpm. b) the corresponding tangential force acting on gear A Please include the free body diagram if necessary.arrow_forward
- Consider a slender rod AB with a length l and a mass m. The ends are connected to blocks of negligible mass sliding along horizontal and vertical tracks. If the rod is released with no initial velocity from a horizontal position as shown in Fig.A, determine its angular velocity after it has rotated through an angle of θ (see Fig B) using the conservation of energy method. (Hint: Moment of inertia of rod about G = (1/12)ml2 The kinetic energy of a rigid body in plane motion isarrow_forwardAn aeroplane makes a complete half circle of 50 metres radius, towards left, when flying at 200 km per hour. The rotary engine and the propeller of the plane has a mass of 400 kg with a radius of gyration of 300 mm. The engine runs at 2400 r.p.m. clockwise, when viewed from the rear. Find the gyroscopic couple on the aircraft and state its effect on it. What will be the effect, if the aeroplane turns to its right instead of to the left ?arrow_forwardThe 250 g disk shown spins at the rate w1 = 750 rpm, while axle AB rotates as shown with an angular velocity ω2 of 6 rad/s. Find the Kinetic energy of the disk with this information.arrow_forward
- Inside a machine, two gears, A and B, HINGED at their centers, are meshed with each other such that gear A transmits torque and speed to gear B. Gear A has a mass mA=2 kg, radius rA=175 mm, and radius of gyration kA=150 mm. Gear B has a mass B=5 kg, radius rB=525 mm, and radius of gyration kB=400 mm. From rest, a counter-clockwise couple M of constant magnitude 6 Nm is applied to Gear A. Which of the following is closest to the magnitude of the angular acceleration of gear B, in radians per square seconds (rad/s2)?3.0044.814.9445.6arrow_forwardA rotating shaft carries four masses A, B, C and D which are radially attached to it. The mass centres are 30 mm, 38 mm, 40 mm and 35 mm respectively from the axis of rotation. The masses A, C and D are 8 kg, 6 kg and 5 kg respectively. The axial distances between the planes of rotation of A and B is 400 mm and between B and C is 500 mm. The masses A and C are at right angles to each other and mass A is positioned at 0 degrees. 1)Show the position of masses in shaf 2)Determine the angles between the masses B and D from mass A for a complete balance. 3)If the mass are balance calculate the axial distance between the planes of rotation of C and D 4)Calculate the magnitude of mass Barrow_forwardA rotating shaft carries four masses A, B, C and D which are radially attached to it. The mass centres are 30 mm, 38 mm, 40 mm and 35 mm respectively from the axis of rotation. The masses A, C and D are 8 kg, 6 kg and 5 kg respectively. The axial distances between the planes of rotation of A and B is 400 mm and between B and C is 500 mm. The masses A and C are at right angles to each other and mass A is positioned at 0o. 1. Determine the angles between the masses B and D from mass A for a complete balance. 2. If the mass are balance calculate the axial distance between the planes of rotation of C and D. 3. Calculate the magnitude of mass Barrow_forward
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