god laws of physics, this is literally my favorite meme of all times!
Galileo ala L.A. Noire
is it mr^2 omega and not some other weird formula that is conserved? Why not mr^3 omega or mr^2 omega^2 ?
This is a great question. And to be honest, there is no intuitive answer as to why it is defined this way or that.
Conservation laws can be understood better through the Lagrangian formulation of classical mechanics.
That’s the conservation of momentum for a free particle. It means that this quantity mv remains constant with time (not m2v, not m2v2 ,just mv).
And similarly for a rotating body, one can find that the quantity that remains constant wrt time is the angular momentum.
And that’s the best rationale using modern physics that can be provided for why Angular momentum takes the form that it does.
Any other form would just not be conserved. Sure, you can construct a Lagrangian that would give you the form that you need but that would not represent anything physical !
Hope that answers your question. Thanks for asking !
** If you have not heard about Lagrangian formulation of classical mechanics, the wiki article on Principle of Least action is a really good place to start..
The principle of Least/Stationary action remains central in modern physics and mathematics, being applied in thermodynamics, fluid mechanics, the theory of relativity, quantum mechanics, particle physics, and string theory.
If unit vectors always scared you for some reason, this neat little trick from The story of i by Paul Nahin involving complex numbers is bound to be a solace.
It allows you find the tangential and radial components of acceleration through simple differentiation. How about that!
Have a good one!
** r = r(t), θ = θ(t)
We are starting a new segment on the blog where we recommend one or two books in Math or Physics that everyone can read.
You are absolutely welcome to share your comments and reviews here once you are done. Also, if you would like us to check a book out, do let us know too!
Have a good one!
“For someone who doesn’t surf in tropical waters and doesn’t go backcountry hiking and camping where bears are prevalent, it’s true: your odds are trillions-to-one that you’ll get both bitten by a bear and a shark in your lifetime. But behavior and risk-exposure matter. It’s not surprising news when someone gets bit by a snake: it happens about 8,000 times per year in the USA alone. It’s not surprising when a surfer gets bit by a shark; surfers are the most likely people to receive shark bites and it happens dozens of times a year. And it’s not surprising to encounter a hungry black bear in the back country woods. And finally, it’s not surprising to survive all of these, as it’s very uncommon for any of these encounters to be fatal.
Dylan is certainly an unusual case, but in every case, he put himself in the most at-risk group for these types of encounters.”
Earlier this week, it was reported that a young man named Dylan McWilliams was bitten by a shark while surfing in Hawaii. This wouldn’t be such a big deal on its own, but last year Dylan was bitten by a bear while camping in Colorado, and two years before was bitten by a snake. Is he just the unluckiest person on Earth, who overcame astronomically small odds to have all three of these things happen to him? Or are the odds, given his behavior and location and circumstances, far higher than a naive calculation would indicate?