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

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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 0 moving with constant velocity v relative to S . 4. Newtonian mechanics: the transformation of coordinates is r 0 = r - v t ; t 0 = t This is called a Galilean transformation. Velocities transform as u 0 = u - v 5. The momentum (rectilinear motion) is p = m ˙ r and in S 0 , p 0 = p - m v ; the acceleration is the same in both frames ¨ r = ¨ r 0 . Newton’s 2nd law remains invariant F = d p /dt F 0 = d p 0 /dt 0 ; t 0 = 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 0 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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