MECHANICS (1) Mechanical Quantities

Mass, force, density, momentum, energy, action, power, stiffness, pressure, viscosity, etc. The bestiary of physics includes myriads of creatures, but they are cast from the same mold. All these mechanical quantities can be understood as various mixtures of space, time and matter, with dimensions of the form M.L^x.T^y, where M, L and T are the dimensions of mass, space and time. This shared structure allows a representation of the mechanical quantities in a plane with coordinates x and y. Moreover, since x and y are usually integers, the standard mechanical quantities can be arranged into a table, which is the perfect cheat sheet for students and a great guide for teachers and researchers. In this first video of this series on mechanics we give an overview of this table of standard mechanical quantities, and we are calling on you to help fill the gaps. The rest of this series on mechanics will show how to use this table to understand space, time and their relationship, from a mechanical perspective.
www.numbersnat...
Contribute to the table of mechanical quantities on wikipedia:
en.wikipedia.o...
Review covering episodes 1 to 8:
doi.org/10.103...
arxiv.org/abs/...
Authors:
Marc-Antoine Fardin (Institut Jacques Monod, CNRS, Université Paris Cité)
Mathieu Hautefeuille (Institut de Biologie Paris-Seine, Sorbonne Université)
Vivek Sharma (Department of Chemical Engineering, University of Illinois at Chicago)
The thumbnail is based on the gif by Oliveirasjeh, displayed at the beginning of the video:
tenor.com/view...
Copyright Disclaimer under section 107 of the Copyright Act 1976, allowance is made for “fair use” for purposes such as criticism, comment, news reporting, teaching, scholarship, education and research

[@ThomasHollis1]

Absolutely love this table, never thought about it this way!

[@Erne0502]

Great explanation! What about x, y being fractions?

[@naturesnumbers]

And what about x and y being irrational? We will address these fascinating questions in future videos on this series. But first we'll ask about integers exponents but outside of the range where quantities have been named. Can't we have mechanical quantities with y>0?