If something is rotating, how do you know when you use the Principle of Work and Energy or Angular Momentum?

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If something is rotating, how do you know when you use the Principle of Work and Energy or Angular Momentum?

In: Physics

This is a very broad question, so it is a bit difficult to give a completely general answer. In principle, you always need to use both since both angular momentum and total energy are conserved. There are shortcuts, though. For example, if the work done on a body is zero, then its potential energy will never change, so the conservation of energy is trivial since it’s just always all in kinetic energy. So, say I have a ball on a string and I’m swinging it in a circle and after some time I cut the string. The only force acting on the ball is the tension on the string and since it is circular motion, this force won’t do any work on the ball. So, I can just use conservation of angular momentum in this case. Hopefully that helps? Like I said, it can be hard to generalize a statement like this.

I usually just start with considering what’s conserved. Momentum being the simplest. Linear and angular momentum are both conserved, and from there we can convert to work and energy.