Does anyone know of a reference that uses only Maxwell's equations to solve the problem of a moving point charge (non relativistically) and the corresponding Magnetic field? I want a solution that does not involve doing a Lorentz transformation. Beginning to think it cannot be done!
Suppose you had 2 equal point masses, one at r and one at 2 r. The moment of inertia is m rsq + 4 m rsq or 5 m rsq. If I place both masses at the center of mass at 3/2 r, then the moment of inertia is 2 m x 9/4 rsq or 4.5 m rsq. I think this is where the confusion lies?
This might help clear up the question. Suppose a force F is applied perpendicular to the rod at a distance of 1/2 the location of the center of mass from the center. What is the angular acceleration?
Interesting thought experiment, as the speed of light is slower in a medium, it is only c in free space. For example, the speed of light in a metal is zero. Seems like we could theoretically create a material where the speed of light is very slow. You might think about how that would be done.
You are on the right track, I see it as torque = (moment of inertia) x angular acceleration.
S is force, r is radius, 1/2 m rsq is moment of inertia, and a is linear acceleration, a/r is angular acceleration.
First take second derivative of x with respect to t to get acceleration which we will call z.
Then use dz/dx = (dz/dt)/(dx/dt)
Looks messy, but technically correct. In the final result, substitute for x where it appears.
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