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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 confidence 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 field 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 satisfied for each component of linear momentum. 3. Conservation of angular momentum : If we define the the angular momentum L r × p (34) and the torque -→ τ r × F (35) This can be written: -→ τ = r × m ˙

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

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