Let's Learn Physics: Coordinates? What Coordinates?

Dealing with a fixed set of coordinates can be clunky and inconvenient, but in Newtonian mechanics, this is often what we have to do. Then, using various tricks and logical gymnastics, we can work out sensible equations of motion. However, this becomes very difficult when systems start to get complicated. So, wouldn't it be great if we could figure out a system where we can choose whatever coordinates will be most convenient to the problem? This is exactly what we will find in Hamiltonian mechanics: a completely coordinate-independent framework of classical mechanics!

[@yuvalbechar5429]

hi I have a question about other video of you (cant remember which one so I'm asking here). In Noether's Theorem every continuous symmetry result conservation law. In Einstein spacial relativity no matter what speed your system moving you see the same physics is this a symmetry? If so what the conservation law? If not how so?

[@zapphysics]

@yuval bechar this is an excellent question. There does exist a Noether charge associated with Lorentz boosts, but it is sort of redundant. The conserved quantity that one finds corresponding to boosts is (tp - xE) where t is the time, p is the spatial momentum, x is the spatial position, and E is the energy. Since boosts will only be a symmetry for inertial systems, we know that p must be constant and we also know that the total energy, E, is conserved as well. So, when we take a time derivative and set it equal to zero, we get p - vE = 0 where v is the spatial velocity. We can solve this to find v = p/E. This is all that this conserved charge is telling us, but we can find this exact same relation by other means as well!

[@yuvalbechar5429]

@@zapphysicsThank you for your answer, youre a great teacher.

[@yuvalbechar5429]

@@zapphysics this is for units where c=1 right what so E=m therefor p = mv. its make so much sense wow. thank you.

[@nzuckman]

Bless u sir

[@bee8017]

this channel is fantastic may you have the old gods blessings

[@darmayuda4157]

Pls u teach to the point in derivative formula so not so take long time unnecessary long conversation, only explain shortly important thing in derivative formula