In my notes we are using polar coordinates, sor=(xcosy,xsiny) implyingr(dot)^2=x(dot)^2 + (x^2)(y^2)

so L= 0.5m(x(dot)) + (x^2)(y^2)) - U(x,y) (we aren't given exactly what the potential is)

I understand that the generalised momentum of x= mx(dot)

.................................................. ...........of y= m(x^2)y(dot)

but then it says the gen. mom. of x can be interpreted as the radial component of the linear momentum, and the gen. mom. of y is angular momentum. I understand that the angular momentum can be checked using the definition, but is there any way you could notice this without checking? (i.e. is it something about the formulas for gen. mom. of y that means it is the angular momentum)?

Sorry for the essay