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I think every motions could be determined by Newtonian Mechanics, but why do we need rotational mechanics, or fluid mechanics?

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    $\begingroup$ Re I think every motions could be determined by Newtonian Mechanics - This question was asked and answered over 100 years ago, and the answer is no. Re why do we need rotational mechanics, or fluid mechanics? Because those are important phenomena. $\endgroup$ Jun 2, 2018 at 10:37

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Push a wheel, applying a force F... yes, F=ma is still valid, but you now have to consider that as the wheel rotates, different points on the wheel move at different speeds (points on the outside move faster than points near the center).

Sure, you can describe the motion of each point using linear mechanics, using just F=ma, but now each point has a different acceleration, and you don't have a nice way to describe the motion of the whole wheel. Rotational mechanics introduces angular acceleration and lets you say $\tau=m\alpha$, which describes the whole wheel very nicely.

So basically, we develop these other formulations of mechanics because they are more natural for describing certain situations. Note that "rotational mechanics" is still Newtonian mechanics - it's just not linear mechanics. Fluid mechanics is also Newtonian mechanics, just further developed so that it can better describe the motion of fluids (rather than considering the motion of every individual particle in a fluid).

Something like Lagrangian mechanics is actually a very different concept from Newtonian mechanics, although it turns out to be equivalent, and is used because it is more convenient for non-Cartesian coordinate systems.

Finally, quantum mechanics is necessary for describing quantum phenomena because there, Newtonian mechanics are simply wrong. Same goes for relativity.

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