I'm wondering whether angular momentum is just a convenience that I could hypothetically solve any mechanics problems without ever using the concept of angular momentum.
I came up with this question when I saw a problem in my physics textbook today. In the problem, a puck with known velocity hits a lying stick. The puck continues without being deflected, and the stick starts both linear and angular motion. There are three unknowns: velocity of puck and stick after collision, and the angular speed of the stick. So, we need three equations: conservation of linear momentum, kinetic energy, and angular momentum.
So, for instance, is it possible to solve this problem without using angular momentum?
Also, how would a physics simulator approach this problem?
Best Answer
If your criterion for something being a convenience is that you could solve problems without it then everything in physics is just a convenience.
There are an infinite number of possible mathematical formulations. So, in principle, it should be possible to convert any mathematical problem into a different formulation that avoids the use of any specific concept that you would like to avoid (or at least hides it so that it is not apparent that you are using the concept).
That said, angular momentum is conserved and it is related (by Noether's theorem) to the fact that the laws of physics are symmetric under spatial rotation. Both conserved quantities and symmetries are very important in modern physics. So even if you classify it as a convenience, it is one of the most important and pervasive conveniences in physics.