The Senses

Everyone knows the classic five senses: sight, hearing, touch, taste, and smell. But do we not sense more than that? In fact there are quite a few additional senses we could include. Here are a few:

Temperature - We sense temperature, but it's worth noting that we don't sense the temperature of other things, only the temperature of our own bodies. This is why steel will feel colder than paper even if they are the same temperature. The steel is much more effective at cooling our skin, and our skin temperature is what we actually sense.

Motion - More precisely acceleration. Each ear contains two accelerometers. One measures vertical acceleration and the other, horizontal. They work by feeling with a hair when a weighted membrane is stretched by inertial forces. Note that we cannot detect velocity. Cruising at high speed in a car doesn't really feel different from standing still if the ride is smooth enough. For that matter nor does speeding through space on a planet.

Body Position, Proprioception - If you block your other senses and have someone change the position of your arm, you will be able to at least somewhat detect the change and report the new position. This awareness is achieved thorough sensors in your muscles and joints that report when and how much they are being stretched.

Spinning Things

Conservation of momentum (previously discussed) can be extended to spinning things. When something spins in place, the object as a whole is not going anywhere, but the individual bits (each with some small mass) are moving at different speeds around the axis, with bits going faster the farther they are from the center. Conservation of momentum applies to each of those bits, so it also applies to them all together. When we talk about this summation of momentum in a spinning situation we call it angular momentum and give it the symbol, L.

So L = I x Ω, where I is a measure of the thing’s shape. If there’s a lot of the thing far from the spinning axis, I is big. Ω is how fast it’s spinning, like ten turns per second.

The cool thing here is that L is constant, so if the shape of the spinning thing changes and I increases or decreases, Ω has to change in the opposite direction.

This is very useful. Think about an ice skater going into a spin. At the start, they have arms way out, one leg trailing way back (big I), and are turning very slowly (small Ω). When they pull their arms and legs tightly in to the center, I gets much smaller, so Ω has to get much bigger - they spin fast!

Let’s see it an action:
Figure skater
Cats falling 
At the playground 
And this guy at taco bell 

Decimate

Decimate is one of the most egregiously misused words today. The difference between intended and actual meaning is almost as great as with literally/figuratively, the true meaning is right there in the word, and the historical use is pretty amazing and not to be forgotten.

Modern usage is typically that to decimate means to drastically reduce, similar to annihilate. In the historical usage decimate meant to reduce by 1/10th, actually a fairly small reduction.   
Language is a fluid and evolving thing, and words may change meaning over time, but this example seems unfortunate. 

Note that "decim" in decimate? As with decimal, or decibel, it comes from the Latin word decimus, meaning 1/10th. Note decibel actually means 1/10th of a Bel, the actual unit of sound intensity, named for Alexander Graham Bell. Since the original meaning can be guessed just from it’s spelling, it’s a bit confounding that it has managed to drift so drastically. Note that annihilate is more true to it’s construction, with that Latin "nil" inside meaning “nothing.”

The final reason the misuse is a shame is that the original use is a remarkable and more unique idea. About 25 centuries ago, the Roman army came up with a clever and horrible punishment for mass desertion. Typically, desertion would be punished by death, but they did not want to lose their own soldiers en mass. And, these being fighting men, such a punishment may be difficult to enact on a large group. The solution was to randomly sentence one in ten of the offenders to death. The whole mass would feel the real fear of punishment, all would feel the loss of people they knew personally and take it to heart, and those spared could be counted on to not rebel, and even to help enact the sentence under orders. 

That punishment has been applied as late as the first world war. The word was also used to refer to the tithe (typically 1/10th of one’s income) staring probably in the 1600’s, and the latest use as referring to a massive reduction seems to have arisen in just the last 100 years or so.

Meander

If we have some kind of slope and deposit a drop of water on it, the water will run directly down the slope. It won't go up for a bit before turning down. It won't run across the slope a ways. It will go as straight down as possible. So why is it that rivers, which are just water running down a slope, meander?

When I was a kid I learned an explanation that was neat, plausible, and wrong: That the ground isn't perfectly smooth, so as soon as the flow bends around an obstacle you have a curve where water is flowing slowly on the inside and fast on the outside. Then the outside erodes more than the inside (which is actually depositing material instead of eroding because of water slowing down) and the curve gets bigger and the process continues getting more extreme until you get big meanders.

There is a major problem with that explanation, in that water does not flow more quickly at the outside of a bend, it flows more slowly. This is vortex flow. Think of a whirlpool in a bathtub. That water is flowing in a curve around the drain with the water on the inside edge right at the drain going very fast and the water toward the outside far away from the drain barely moving. The action of making the curve bigger actually comes from a secondary flow. The surface of the flow around a bend is a bit higher on the outside edge. It's like a bit of slosh as the bank pushes it around the curve. Well if the surface is higher on the outside, that means there is higher pressure on the outside than the inside. That pressure drives a secondary flow of water down the outside bank, across the bottom of the river toward the inside, and then back across the surface to where it started. This flow carries any eroded sediment from the outside bank to the inside. This is how you get the difference in erosion that leads to bigger meanders.

click for video

The same explanation solves the Tea Leaf Paradox. When you stir a cup of tea with bits of tea leaves on the bottom, intuitively you may expect the leaves to all be driven to the outside edges. But no, they collect in the middle. The tea leaves are like river sediment and both are driven by secondary flow in a vortex.

click for real life timelapse

An interesting feature of this system is that there is positive feedback. Once a curve starts, it just keeps getting more and more extreme. The more curvy, the more the curve increases. Well, there's a limit to how far a river can curve because eventually the curves will intersect each other. When that happens the river will kind of short circuit and cut through that intersection instead of going all the way around the curve. That's how we get oxbow lakes. They are old river meanders that have been cut off from the main river flow.

Tire Pressure

Imagine you've lost a bet. Your “friend” is now going to run over your thumb with his car*, a 1996 Honda Accord. (This, by the way, was the most stolen car in 2012 (8637 cars according to the NICB Hot Wheels report)). He (I assume it’s a he) goes inside to get his video camera (of course). What can you do to the car in the seconds he’s gone to help this go better for you? 

One idea would be to let as much air out of the tire as possible. If the rubber itself is very flexible**, the force your thumb will see is limited by the pressure the tire can apply to the area of your thumb. The less tire pressure, the less force. The force the tire supports overall is the same (about ¼ of the car), but it’s supported over more area as the tire flattens and is in contact with more road. So if it’s flat enough hopefully more of the tire is born by the road and less by your digit.

That car weighs about 3000 lbs. The tire width is 7.28”. Normal tire pressure is about 35 psi. So normally (3000 lbs) / (4 tires) / (35 psi) = 21 square inches of tire is in contact with the road (tire width is about 7 in, so that’s about 3 in of contact length). If your thumb is 0.625 in wide by 2.5 in long its area is 1.6 square inches. That’s 8% of the contact area, so you’ll get something like 8% of the wheel load, or 57 lbs. If you can reduce the tire pressure to 10 psi, more like 75 square inches will be on the road, but your thumb is the same 1.6 sqin, so you only take 2% of the load, or 16 lbs: much better.

*   Do not do this.
** Actually, the tire rubber is not perfectly flexible, so those forces will be higher (so do not try this), but the idea of less pressure meaning less force under a given area of the tire is still valid. Also, if too much air is let out the steel rim could come into play and the result would be very bad (so do not try this). Also, we’re not even talking about the pinching and abriasian that could occur as the tire goes up one side and down the other (so dont’ try this)

Second Law

You have a spool of rope laying on it's side. The rope is passing under the central axle and to the right toward you. You pull slowly on the rope directly to the right. What will happen? Will the spool roll away from you to the left, or toward you to the right?

Despite the common intuition that such pulling will cause the spool to spin counterclockwise and roll to the left, in fact it will roll to the right (and wind up the rope you are pulling). Try it.

One way to think of why this must be true is through Newton's Second Law of Motion. Newton's second law is one of the most simply stated yet powerfully predictive ideas in physics. It is:

F = M * A

Where F is the force exerted on an object. This is a vector, so it is a direction and a magnitude.
M is the mass of the object.
And A is how the object accelerates, also a vector.

This means that if you pull on the spool to the right (F), and nothing else is pushing or pulling on it*, the acceleration vector (A) must be in the same direction and just scaled by the mass, M.

*Gravity is pulling it down, but the ground is pushing it up just the same, and our pulling is not at all in the same direction, so it shouldn't affect anything. Also friction is pushing left, but by its nature friction can't be greater than our force, F. Since we're just talking about the direction and not magnitude of the motion, it's fine to ignore it.

Momentum

We previously talked about conservation of energy - an idea that is a very powerful way of understanding the world. However, actually auditing every form of energy and trying to find out how much goes to what form can be very difficult. Sometimes it helps to apply another, similar rule: Conservation of momentum.

Momentum is a thing’s mass x velocity

Like energy, momentum remains constant unless acted on my some extended outside force. Let’s look at a famously bad example from Lethal Weapon. When Riggs, the protagonist, starts to get too close to the truth, one of the villains drives by and shoots him. In the movie, the blast propels Riggs off his feet, into the air and through a window. Conservation of momentum gives us a simple way to see how plausible this is. Let’s compare things right before and after impact. Before, you have Riggs standing still and the cluster of shotgun pellets flying toward him. After, you have Riggs with the cluster of pellets embedded in his bullet-proof vest moving at some speed we’d like to figure out. 

Before:
Riggs’ momentum = (150 lbs) x (0 mph) = 0 lb-mph
Shot’s momentum = (0.05 lbs) x (820 mph) = 41 lb-mph

After:
41 lb-mph = (150.05 lbs) x V
V = 0.3 mph

That’s pretty close to a giant tortoise pace; ten times slower than average human walking pace. He may stagger, but he definitely will not go flying through the air.