PHY354H1 Lecture Notes - Cross Product, Momentum, Conservation Of Energy
Document Summary
Lecture 22: energy conservation in 3d, cen- tral forces: relevant text sections: morin 5. 3, 7. 1-7. 2. Must only be functions of position: (cid:126)f ((cid:126)r) but must also meet the requirement that: (cid:126)f = 0 (1) i. e. that the curl of the function is 0. In order to prove this, you need to use stoke"s theorem (which you will learn in multivariable calculus near the end of the course). I will assume you haven"t seen this yet and therefore you are not responsible for proving the above. But you are responsible for being able to use equation (1) to test whether a force is conservative. You can read about the proof in the text if you like: since some of you haven"t seen the curl before, its just a cross prod- uct of the gradient operator and a function. I"ve provided the formula in the supplementary notes and deepak will cover some examples in next monday"s lecture.
