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Something I put together for my classical mechanics course. The surface is the minimum area surface spanning two rings as they are separated.
CALCULUS EQUATIONS & ANSWERS
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Work and Impulse might seem a lot like each other. We take integrals to get to each, and take derivatives to get back to each.
What's different is the dimension. Impulse (or change in momentum) is the area under the curve on a (time, Force) graph and work (or change in energy caused by this force) is the area under the curve on a (distance, Force) graph. Both integrals are useful for different things, and you should pay close attention to the distinction as we continue to work through these issues.