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: Dynamics
- For an axisymmetric body under no force, prove (a) that the rate of retrograde precession can never be less than twice the rate of spin of the body about its axis of symmetry, (b) that in Fig. 18.24 the axis of symmetry of the body can never lie within the space cone. Reference to Figure 18.24:arrow_forwardAs shown in Figure 5, disk A is free to spin about the bar B, which is perpendicular to the disk and rotates anti-clockwise with a constant angular velocity w, = 1 rad/s about z-axis. The length of bar B is L = 2/3 m, and the radius of the disk R = 2 m. Assume that the disk spins without slipping on the surface. 1) Determine the absolute angular velocity of the disk aa: 2) Determine the absolute angular acceleration of the disk a4; 3) Determine the velocity and acceleration of point P on the disk. Vp, ap Pi L R 0 = 30° Figure 5.arrow_forwardI need the answer as soon as possiblearrow_forward
- cord] 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_forwardA 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_forward
- An open circular cylinder of 20 cm diameter and 120 cm long contains watr up to a height of 80 cm. It is rotated about its vertical axis at 400 rpm. Find the difference in the total force in N at the sides of the cylinder due to rotation. a.14.52b.1256.17c.568.73d.2465.45arrow_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(Three-Dimensional Motion) A homogeneous 20-cm-diameter disk has a mass of 1 kg and is placed on apedestal so that the assembly precesses in a horizontal plane as shown. If theprecessional rate is 20i rpm, determine the magnitude and direction of the spinof the disk about its own axle.arrow_forward
- 3 The object below can rotate in the plane of the page about a fixed axis at A. The object is symmetric about A in the vertical and horizontal directions. A time=0, the object is rotating counterclockwise at 5 rad/s. The material has a uniform area density of 120 kg/m². a. What is the mass moment of inertia of the object about Point A? b. The net moment applied about Point A is shown on the graph. What is the angular velocity, w₁5, of the object at t-15 seconds? MA [Nm] 16 0.15 m 120 kg/m² 0.3 m H wo = 5 rad/s A 0.8 m 0.3 m 0.6 m 0 -8 0.15 m 10 15 time [s]arrow_forwardi need the answer quicklyarrow_forwardA shaft carries three masses A, B and C of magnitude 200 kg, 300 kg and 400 kg respectively and revolving at radii 80 mm, 70 mm and 60 mm. The angles between these masses are A to B 120° and B to C 70°. If the balancing masses revolve at a radius of 100 mm, find their magnitudes and angular positions. All masses rotating * .in the same planearrow_forward
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