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.

Body English

Perhaps you've heard of "putting english on" a ball to cause it's path to curve (See the Magnus Effect). What about this is English? Especially since it seems to be almost exclusively an American term. The English don't refer to it as english; they call it "side."

There are two possible explanations I like:
1. The first relatively widespread and dramatic ball curvature Americans were exposed to was thorough English pool sharks in the 19th century.
2. It comes from the French word "anglais," which refers both to the geometry concept and to the Angles who were early settlers of England (think Anglo-Saxon).   

The earliest example of the term in print seems to be by Mark Twain in The Innocents Abroad:
"the cues were so crooked that in making a shot you had to allow for the curve or you would infallibly put the "English" on the wrong side of the ball"

A similar sounding, but separate term is Body English. This describes the physical gestures the athlete may perform after releasing the ball to encourage it to follow the desired path. Our President demonstrates above.

This may be an expansion of the term above, in that both seek the same result though different means, or it may come independently from one's gestures being a kind of body language, or body English.