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PHYSICS
PHYSICS

... Newton’s Law of Universal Gravitation Objects attract other objects with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them m1 m2 F = G ...
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... • The sum of all the Forces acting on the system is equal to the total mass of the system times the acceleration of its center of mass. • The center of mass of a system of particles (or objects) with total mass M moves like a single particle of mass M acted upon by the same net external force. ...
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... Q30. A physical pendulum consists of a uniform solid disk of radius R = 2.0 cm supported in a vertical plane by a pivot located at the edge of the disk. The disk is displaced by a small angle θ and released from rest. What is the period of the resulting simple harmonic motion? A) 0.35 s T072: Q27. A ...
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... associated with an electrically charged particle moving through space-time is associated with the response of the vacuum (i.e. space-time and its structure - at the microscopic level) to the passage of the electrically charged particle through space-time! This says something very deep about the fund ...
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< 1 ... 46 47 48 49 50 51 52 53 54 ... 446 >

Newton's theorem of revolving orbits



In classical mechanics, Newton's theorem of revolving orbits identifies the type of central force needed to multiply the angular speed of a particle by a factor k without affecting its radial motion (Figures 1 and 2). Newton applied his theorem to understanding the overall rotation of orbits (apsidal precession, Figure 3) that is observed for the Moon and planets. The term ""radial motion"" signifies the motion towards or away from the center of force, whereas the angular motion is perpendicular to the radial motion.Isaac Newton derived this theorem in Propositions 43–45 of Book I of his Philosophiæ Naturalis Principia Mathematica, first published in 1687. In Proposition 43, he showed that the added force must be a central force, one whose magnitude depends only upon the distance r between the particle and a point fixed in space (the center). In Proposition 44, he derived a formula for the force, showing that it was an inverse-cube force, one that varies as the inverse cube of r. In Proposition 45 Newton extended his theorem to arbitrary central forces by assuming that the particle moved in nearly circular orbit.As noted by astrophysicist Subrahmanyan Chandrasekhar in his 1995 commentary on Newton's Principia, this theorem remained largely unknown and undeveloped for over three centuries. Since 1997, the theorem has been studied by Donald Lynden-Bell and collaborators. Its first exact extension came in 2000 with the work of Mahomed and Vawda.
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