I didn't understand what you mean,
d^2 f/dx^2= -f*(2xk^2+2kwt)-2k^2*sin((kx+wt)^2)
and nothing here suggest that there exist a constant A that for every t and every x
d^2 f/dx^2=Af.
i actually think not, cos(x^2) or cos(2x*t) is not an harmonic wave.
in general, an harmonic function f is a function that gives f''=A*f when A is a constant. the function you gave do not fulfil this requirement.
The answer to the question is that the angular momentum is a constant in relation to time, but the partial derivative in r is not zero. In other words:
\frac{dl}{dt}=0,
\frac{∂l}{∂r}\neq0.
I do think that:
\frac{dl}{dr}=0.
What about the heating of the cylinder at step 2? Maybe that's where the Energy comes from. If it does than you will not have any problem.
didn't you say that it's an insulated system? If it is, how does the atmosphere heats it? If it's not, energy can move from the system to the atmosphere.
In Newton's problem,and other central force problems in Classical Mechanics, you can get with decreasing the center of mass movement to the lagrangian:
L=1/2m(r' ^2+r^2 \varphi'^2)-V(r)
because \varphi is cyclic, you can write:
\frac{d}{dt}(mr^2 \varphi')=0
or, defining the angular...
It's just a selection of unit's, you can't explain relationships between units like c and m/s. It's not a coincidence just a measurement. the meter is a unit previously connected with Earth circumfence, so obviously it isn't related with a universal property like the speed of light. for more...
I would say that it's because the light is a electromagnetic wave, obe that oscillate both in the electric field and in the magnetic field. But thwe first estimation of both epsilon and miu dates before the description of electromagnetic waves.
Coulomb's Constant is defined by the speed of light c, in that way:
C=\sqrt{\mu_{0}\epsilon_{0}} where \mu_{0} is permeability of free space, defined as \ 4\pi\ \times\ 10^{-7} and thus \epsilon_{0} is well defined, κ_{e} is\frac{1}{4\pi \epsilon_{0}}. So if we know c from experiments we can...