Concept explainers
Show that for an axisymmetric body under no force, the rates of precession and spin can be expressed, respectively, as
and
where HG is die constant value of die angular momentum of the body.
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Vector Mechanics For Engineers
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- HW2 A uniform disc of 80 mm radiuse has a mass of 2000 g. It is mounted centrally in bearings which maintain its axle in a horizontal plane. 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 as shown in 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. +y +Zarrow_forwardI need the answer as soon as possiblearrow_forwardcord] w = 2.2 rad/s 5 x = 604 rad(5²5 (constant) 1.5 m has A disk is to a fixed axis of rotation through its center as shown, and a cord wraps around it, and attaches to a block. Assuming that the disk's initial angular velocity is w = 2.2 rad/s CCW, and that its angular acceleration is α = 6₁4 rad /s² cew (and that x is constant),"" fined (a) the acceleration of the block (mag and direc) (b), the velocity of the block after 2.8s (mag and direc) (c) the distance traveled by the block during that timearrow_forward
- A spinning top consists of a ring (which can be treated as a cylindrical shell) of mass m = 0.52 kg and a radius of 60 mm is mounted on its central pointed shaft with spokes. The spokes and pointed shaft have negligible mass meaning that their inertia can be neglected. The top has a spin velocity of 10,000 rev/min and is released on a horizontal surface with the point at O remaining at a fixed point. Assuming that the spin angular velocity is high when compared to the precession, determine the magnitude of the precession angular velocity of the top. 15° 60 mm 80 mm 10000 rev/min O 1.2 rad/sec 0.6 rad/sec 0.2 rad/sec 2.1 rad/secarrow_forwardA spinning top consists of a ring (which can be treated as a cylindrical shell) of mass m = 0.52 kg and a radius of 60 mm is mounted on its central pointed shaft with spokes. The spokes and pointed shaft have negligible mass meaning that their inertia can be neglected. The top has a spin velocity of 10,000 rev/min and is released on a horizontal surface with the point at O remaining at a fixed point. Assuming that the spin angular velocity is high when compared to the precession, determine the magnitude of the precession angular velocity of the top. 15° 60 mm 80 mm 10000 rev/minarrow_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_forward
- A shaft carries four masses A, B, C and D of magnitudes 18 kg, 15 kg, 27 kg, and 22.5 kg respectively and revolving at radii 20 mm, 25 mm, 30 mm and 15 mm respectively. The masses are rotating in the same plane. The angular position of masses B, C and D are 60 degrees , 135 degrees and 270 degrees from mass A. Find the magnitude and position of the balancing mass at a radius of 50 mm,arrow_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_forwardA yoyo is constructed by attaching three uniform, solid disks along their central axes as shown. The two outer disks are identical, each with mass M = 58 g, radius R = 3.3 cm, and moment of inertia 1/2MR2. The central, smaller disk has mass M/2 and radius R/2. A light, flexible string of negligible mass is wrapped counterclockwise around the central disk of the yoyo. The yoyo is then placed on a horizontal tabletop and the string is gently pulled with a constant force F = 0.25 N. The tension in the string is not sufficient to cause the yoyo to leave the tabletop. In this problem consider the two cases show. In Case 1 the string is pulled straight up, perpendicular to the tabletop. In Case 2 the string is pulled horizontally, parallel to the tabletop. In both cases the yoyo rolls without slipping. In both the cases shown what is the magnitude of the tourqe t excerted by the string about the contact point of the yo-yo wiith the table in N*m. What is the moment of intertia of the yo-yo…arrow_forward
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