Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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A particle P of mass 2m can slide along a smooth rigid straight wire. The wire has one ofits points fixed at the origin ’O’, and is made to rotate in a plane through ’O’ with constantangular speed Ω. Show that r , the distance of P from O, satisfies the equation r ̈ − (Ω^2)*r = 0 Initially, P is at rest (relative to the wire) at a distance a from O. Find r as a function of t in the subsequent motion.
Half ring with internal radius a and external b, with surface mass distribution σ = σ0/r, where σ0 is a constant. Let a point P be at a height h from the plane of the half ring. The escape velocity at P is
Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite? Let T denote the period of revolution of the satellite. Kepler’s third law says that the square of T is proportional to the cube of the major semiaxis a of its elliptical orbit. In particular, if GM D 1, then?
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