vCalc lets you look at the math behind your everyday life. And we get smarter by doing so, seeing the world as it is represented by the math and science, seeing the reality of how it all works.
I like peering into that reality.
There are a lot of REALLY cool stuff on the web these days, departures from the norm that are at your fingertips. This vCalc collection will examine some of the coolest videos and point you to the math behind the cool stuff. The arrival of YouTube videos examining the science behind our universe and the math in our everyday existence has opened up a whole new realm of understanding. The math behind these videos gives you insights that will make the world seem less intimidating. And besides, its fun to watch things blow-up, spin, defy your everyday logic or exhibit some other unusual behavior.
It's fun to see the world as it truly is.
We're going to explore the real math behind some cool YouTube videos here. We're going to look at some of my favorite scientist, engineer, video-journalists' work and the coolest things they have brought us on the Internet.
And by the way, I am a child of the 70s. Cool things are just that -- oool. I will use the adjective liberally throughout and if it seems too dated, you can just translate it in your mind into your own cool-speak.
One of the current hottest places to see really cool stuff, things that will boggle your mind and excite the ingenious side of your brain is Smarter Every Day, a YouTube channel about -- well, it's about whatever Destin is thinking about on any given day.
Destin Sandlin is an aerospace engineer like myself and he thinks about the kind of things I think about. So, I love his videos and maybe his visualization of the world around you will excite you too and head you down a path of growing smarter every day.
Destin has a successful YouTube channel that you can find here: Smarter Every Day You Tube Channel
We'll explore the math behind some of Destin's videos so you'll have an even better appreciation of the cool things that capture Destin's attention.
I believe this video precedes Smarter Every Day, but rockets are cool and I built model rockets as a kid and had a science fair rocket experiment that led me to looking up the science and math behind rockets. Maybe this led me to work in aerospace. Maybe I was just fascinated by the "whoosh". Anyway, the physics concepts exhibited by rocketry are part of your every day, believe it or not. So, let's give you a leg up and give you some of the math/science side-by-side with Destin's video.
Here's the video: How to light a bonfire with rockets.
First, we can take a look at the basic principle. What makes a rocket "go".
Newton's three laws define the basics of motion caused by rocket engines, whether its a model rocket near ground level or an engine applied in a space vehicle. Here's a vCalc calculator that deals with Newton's three laws:
If `|sum_1 vecF_i| = 0`, then velocity = 0
`|sum vecF_"ext"| = m*a`
`F_"(A on B)" = F_"(B on A)"`
Newton's 3rd law expresses the fact -- the law -- that whenever one body exerts a force on a second body, the second body exerts a force equal and opposite to the force the first body exerted. In the case of the rocket engine, the force created inside the combustion chamber of the rocket by the ignited fuel escapes out the back of the engine. That means the force inside the chamber accelerates the expelled gas out the back of the engine.
Here's NASA's explanation of Newton's Third Law as it applies to rocket thrust: Newton's 3rd Law
The total force of combustion on the walls of the chamber expelling the gas out the back causes an "equal but opposite" force on the rocket, propelling the rocket body forward. Nothing is holding the rocket except some slight friction of the rocket on the string in Destin's video, so the rocket accelerates forward and opposite the expelled gas. And that leads to cool things like trips to the moon and bonfires igniting.
As a junior high student, I entered a science fair with a project that involved mice and rockets. I had pet mice. I built model rockets. It was inevitable.
If you'd like to read a discussion of the by-today's-standards not quite socially acceptable experiments on mice, click the following link: Model Rockets and Mice
This experience delved into the basic physics of engine thrust, forces on an accelerating body (a mouse) and even the centripetal force felt by the mouse in a centrifuge.
This video is short and without explanation of the physics but it is really cool. I especially like the curling vortex following the bullet's passage that reflects the effect of the high angular velocity rotation of the bullet as it passes through the liquid.
Projectile motion and ballistic motion is affected by a number of basic physical principles and so contains a wealth of useful examples for applying the laws of physics.
I plan to do a whole series of vCalc equations on the trajectories of bullets (or high speed projectiles). Already in vCalc are the following equations by other authors:
Other ballistics equations and data compiled on vCalc:
This high speed video is awesome. To see what happens when a bullet passes through a bottle and out the bottom of the bottle, check out this Smarter Every Day video by Destin Sandlin. Refer to the math in the previous section for some ballistics information, among other equations scattered about vCalc.
The rotational inertia, or moment of inertia is a measure of the resistance of an object to rotate about a specified axis of the object.
Here's a video that shows Destin's two small accomplices predicting which of two wheels will have the most rotational inertia:
Rotational Inertia Demonstration
Rotational inertia, or moment of inertia depends on the precise shape and composition of an object. The large dimensions of the wheel in this video compared to the added weights which are distributed differently between the two wheels most likely allows us to approximate the wheels as a cylinder or disk rotating along its central, symmetric axis. So, the vCalc equation that applies to this moment of inertia is:
Moment of inertia for a cylinder rotating along symmetric axis
You can see other moments of inertia calculations at: Moments of Inertia and there are numerous others throughout vCalc:
Search vCalc for even more Moment of Inertia equations for different geometric shapes.
The Veritasium YouTube channel is a most excellent set of videos created by Derek Muller addressing many theories of science with practical applications.
Bayes Theorem describes the probability that an event could happen, based on prior knowledge of the event. Bayes’ theorem may allow you to more accurately assess the probability of an occurrence of an event using knowledge of the event.
See the vCalc equation for: Bayes Theorem.
Derek has created a wonderful video that explains how the international standard 1 kilogram mass is being redefined -- this year (2018)!
The kilogram mass was the last SI standard unit to be defined by a physical object (a bar of metal). Now it will be defined by fundamental quantum-related physics constants: Planck's Constant and Avogadro's number. This is an important event impacting science in general so we will devote a vCalc Collection page to it: The Standard Unit of Mass
Watch Derek's video before you jump to the page. The video is awesome.The Standard Unit of Mass
See Derek's excellent video about how the standard mass is being redefined: How we're redefining the kg
In the meantime, check out these constants in vCalc: