When you get into classical mechanics you find that F = ma applies, but the implementation gets into all the math you have. What if you have a system of particles where the coordinate system does not have a uniform force across it but a lumpy potential field. For example, the Milky Way. The astronomy sector of physics is still having trouble modeling that system. Then somebody suggests they have to invoke general relativity. Or, suppose the potential field is electric. Force does not lie along the line between two electric charges if they are moving, but generates magnetic components in some other direction.
Force does not lie along the line between two electric charges if they are moving, but generates magnetic components in some other direction.
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Yeah it's still unbelievable to me how Maxwell figured out his equations.