p09fl35 - Lecture 35 Relativity(23 Nov 09 A Galilean...

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Unformatted text preview: Lecture 35: Relativity (23 Nov 09) A. Galilean transformations 1. Refs: Goldstein Chapter 7, Bergmann Chap 2, Møller Chap 1 2. Inertial frame: in such a coordinate system all bodies not subject to forces are not accelerated. Newton’s first law: in absence of forces, body remains at rest or in straight line uniform motion. 3. Denote an inertial frame by S and consider another coordinate frame S moving with constant velocity v relative to S . 4. Newtonian mechanics: the transformation of coordinates is r = r- v t ; t = t This is called a Galilean transformation. Velocities transform as u = u- v 5. The momentum (rectilinear motion) is p = m ˙ r and in S , p = p- m v ; the acceleration is the same in both frames ¨ r = ¨ r . Newton’s 2nd law remains invariant F = d p /dt → F = d p /dt ; t = t (Add to the Galilean transformation the statement that F and m are invariant). In particular, for 2-body forces derived from a potential, F 1 =- ~ ∇ 1 φ ( | r 1- r 2 | ) we have F 1 = F 1 . 6. Bodies subject to forces have non-zero accelerations. the ratio of force to acceleration is a constant, the mass of the body (an intrinsic, con- stant, parameter of the body)....
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This note was uploaded on 12/14/2009 for the course PHYS 711 taught by Professor Bruch during the Fall '09 term at University of Wisconsin.

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p09fl35 - Lecture 35 Relativity(23 Nov 09 A Galilean...

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