21-71. The space capsule has a mass of 2 Mg, center ofmass at G, and radii of gyration about its axis of symmetry(z axis) and its transverse axes (x or y axis) of k; = 2.75 mand k, = k, = 5.5 m, respectively. If the capsule has theangular velocity shown, determine its precession o andspin i. Indicate whether the precession is regular or retrograde.Also, draw the space cone and body cone for the motion.30%w = 150 rad/s

Write the expression of the moment of inertia of the space capsule in the x-direction. Write the…

Answered: 21-71. The space capsule has a mass of…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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*21-40. Derive the scalar form of the rotational equation of motion about the x axis if N + w and the moments and products of inertia of the body are not constant with respect to time.
The top has a mass of 1 kg and radius of gyration of k, = 25 mm about its axis of symmetry. The top spins and precesses about the ball-and-socket joint at point O. It's transverse radius of gyration about point O is k = 63 mm. The spin velocity is ws = 150 rad/s. • Under these conditions. determine the two possible precession velocities op of the top. Determine the kinetic energy of the top for each of the two possible precession velocities.
The platform AB when empty has a mass of 400 kg centre of mass at G1 and natural period of oscillation t1=3.82 s. If a car, having a mass of 1.2 Mg and centre of mass at G2 is placed on the platform, the natural period of oscillation becomes t1=4.58 s. Determine the moment of inertia of the car about an axis passing through G2.
This is a dynamics question. Answer: v = 7.09 ft/s
21-69. The top has a mass of 90 g, a center of mass at G, and a radius of gyration k = 18 mm about its axis of symmetry. About any transverse axis acting through point O the radius of gyration is k, = 35 mm. If the top is connected to a ball-and-socket joint at O and the precession is w, = 0.5 rad/s, determine the spin w,. 60 mm
The 213-kg wheel has a radius of gyration about its center O of ko = 240 mm, and radius r = 0.4 m. When the wheel is subjected to the constant couple moment M = 85 N·m, it starts rolling from rest. Determine the wheel's angular velocity W (in rad/s) after 4.4 seconds if the wheel has been rolling without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s². M Your Answer: Answer
This is a dynamics problem. One Answer: P = 579 N
21-78. The radius of gyration about an axis passing through the axis of symmetry of the 1.2-Mg satellite is k = 1.4 m, and about any transverse axis passing through the center of mass G, k, = 2.20 m. If the satellite has a known spin of 2700 rev/h about the z axis, determine the steady-state precession about the z axis. 15°
*21-76. The football has a mass of 450 g and radii of gyration about its axis of symmetry (z axis) and its transverse axes (x or y axis) of k. = 30 mm and k, = ky = 50 mm, respectively. If the football has an angular momentum of H, = 0.02 kg m/s, determine its precession o and spin i. Also, find the angle ß that the angular velocity vector makes with the z axis. HG = 0.02 kg - m²/s 45° A
Specifically a dynamics problem. Question in pic below. Answer: omega = 20.35 rad/s
The circular disk of 270-mm radius has a mass of 36 kg with centroidal radius of gyration k = 235 mm and has a concentric circular groove of 105-mm radius cut into it. A steady force T is applied at an angle to a cord wrapped around the groove as shown. If T = 59N, 0 = 29°, μs = 0.08, and μk = 0.07, determine the angular acceleration a of the disk, the acceleration a of its mass center G, and the friction force F which the surface exerts on the disk. The angular acceleration a is positive if counterclockwise, negative if clockwise; the acceleration a is positive if to the right, negative if to the left; and the friction force F is positive if to the right, negative if to the left. m= 36 kg k 235 mm 270 mm T G Ug = 0.08 Uh = 0.07 105 mm.
The shown spool has a mass of 450 kg and aradius of gyration Gk=1.2 m. It rests on thesurface of conveyer belt for which the coefficient offriction m= 0.5. If the conveyer acceleratesat2 1.2m / S and the spools rolls without slipping,determine the tension in the wire and the angularacceleration of the spool

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