Category: maths

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Oh my god laws of physics, this is literally m…

Oh my god laws of physics, this is literally my favorite meme of all times!

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Galileo ala L.A. Noire 

Galileo ala L.A. Noire 

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On the definition of  Angular MomentumAnonymous asked:Why is it…

On the definition of  Angular Momentum

Anonymous asked:

Why
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.

What makes the definition special?

Conservation laws can be understood better through the Lagrangian formulation of classical mechanics.

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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.

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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…

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)

Introducing FYP’s book club

We are starting a new segment on the blog where we recommend one or two books in Math or Physics that everyone can read.

And this month it is : A Mathematician’s Apology by G.H.Hardy which is available for free to download here and here

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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!

This Is How Bad Credit Can Double The Cost Of …

This Is How Bad Credit Can Double The Cost Of Your Next Car

The one question to never answer at the dealer. “How much do you want to pay a month for your car?” This is where they really get you. And by get you, I mean that they sell you a car that you really shouldn’t be buying, given the amount of interest you’ll need to pay. The dealer has every incentive to lengthen your loan term as much as possible; the longer you’re making monthly payments, the more you’re paying in interest. For someone with bad credit, and a 14.99% rate on their car loan, here’s how a longer term lowers your monthly payments, but costs you so much more in the long run.”

When you go to a car dealer to buy a new car, unless you have enough cash to pay for it outright, they’ll always do a credit check in order to offer financing. If your credit score is great, you might get a rate as low as 1.99%, but if it’s less than great, it could be significantly higher. Rates ranging from 4.99% to 14.99% might still seem reasonable, but over the span of years, those extra percentage points can mean thousands or even tens-of-thousands of extra dollars spent in interest. The dealer will try to get you to tell them “how much can you pay per month,” but what you should be negotiating for, other than price, is for every single fraction-of-a-percent you can on your interest rate.

If your credit is less than stellar, beware: it’s going to add thousands of dollars to the price of your next car. Come learn how to negotiate for your money.

What Are The Odds Of Getting Bit By Both A Bea…

What Are The Odds Of Getting Bit By Both A Bear And A Shark?

“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?

What happened to Dylan was unusual, but it’s not nearly as unlikely as you might think. Come get a solid lesson in conditional probability today! (It’s more fun than it sounds!)