class5 - 1.4 Single Particle Conservation theorems Where do...

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1.4 Single Particle Conservation theorems Where do conservation theorems come from? They cannot be proven per se , but are conse- quences of Newton’s laws of dynamics. The conservations theorems must be put to the test of experiment, and if found not to be violated, give a measure of conFdence in the original dynamical laws. That these conservation theorems have been found to be valid in a wide range of circumstances is an important part of the “proof” of the correctness of Newton’s laws, at least in classical and non-relativistic physics. 1. The total energy of a particle in a conservative force Feld is constant in time . Discussed above: see section below. 2. Conservation of linear momentum : The total linear momentum p of a particle is conserved when the total force applied to it is zero. The vector equation ˙ p = 0 is satisFed for each component of linear momentum. 3. Conservation of angular momentum : If we deFne the the angular momentum L r × p (34) and the torque -→ τ r × F (35) This can be written: τ = r × m ˙ v = r
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This note was uploaded on 09/20/2010 for the course AMATH 261 taught by Professor Rogermelko during the Spring '10 term at Waterloo.

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class5 - 1.4 Single Particle Conservation theorems Where do...

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