'Theoria Motus Corporum Solidorum seu Rigidorum', Euler - translated and annotated by Ian Bruce.The moment of inertia of circle with respect to any axis passing through its centre, is given by the following expression:Įxpressed in terms of the circle diameter D, the above equation is equivalent to:.'Euler, Newton, and Foundations for Mechanics', Marius Stan.The moment of a vector quantity $\vec$ is superficial.
We could for example agree to call motion along the direction of one specific sheet of a hyperbolic paraboloid the ' motator'. Thus simply due to the 'importance' of Archimedes, historically talking about other circular motions in a way that allows one to easily compare to Archimedes makes sense, so if we're going to use one word related to the Latin 'moveo' to relate to what is called momentum, we can use another word when talking about specifically rotational motion the way Archimedes set it up. equilibrium means the block on a level have equal importance, non-equilibrium means one will find rotational motion of the level in one direction over the other making one of them more 'important' then the other. The etymology of moment and momentum relate to motion/movement apparently via the latin verb 'moveo' meaning 'to move'.Īpparently the first English use of the word moment meant it in the sense of 'importance' on a lever, i.e.
To appreciate why you would even end up with something like $I = mr^2$ in Newtonian mechanics, it's useful to go back to the meaning of the word 'moment'. If taken literally, saying that $I = mr^2 = r (mr)$ is the 'moment of inertia' of a particle actually implies (see below) that $mr$ is the 'inertia' of a particle, which nobody interprets it as (as the tendency of an object to resist changes in it's motion does not even depend on $r$). If we wanted to understand this quantity $I = mr^2$ which has some definition, the first thing we could do is think about what the definition means. Why is the moment of inertia of a point mass defined as $mr^2$?
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