How fast should you walk through the rain to stay as dry as possible?

You should walk as fast as you can.

The rain wets you in two different ways: by falling on your head and shoulders and by colliding with your front as you walk forward. The amount of rain that lands on your head and shoulders is directly proportional to how long you are in the rain, but the amount of rain that hits your front depends only on the density of the raindrops. Your speed has no effect on the amount of rain that hits your front, but it definitely affects the amount of rain landing on you from above. To minimize the rain dropping onto you, you should walk as fast as you can.

What is the job of a microprocessor inside of a navigation system?

The microprocessor does everything in the navigation system except for activities that require specialized, dedicated electronic circuitry. For a unit based on the global positioning system (GPS), there are specialized circuits to detect and time microwave signals emitted by an array of earth-orbiting satellites and specialized circuits to operate a display and a sound system, but that’s about it. Everything else is done by one or more microprocessors.

Microprocessors now play a dominant role in most electronic devices because microprocessors allow their sophisticated circuits to be reused endlessly for many different purposes. Prior to the microprocessor revolution, electronic devices had to implement separate circuitry for each and every task or process. Nothing could be reused or reassigned, even if it wasn’t doing anything most of the time. With microprocessors, reuse and reassignment is easy and leads to enormous improvements in circuit efficiency. Devices that were once huge, expensive, and power-hungry can now be reduced to a small printed circuit board featuring a tiny microprocessor and a handful of dedicated circuits that are responsible for conveying information to and from that microprocessor.

A navigation system is a fine example of this shift to microprocessor-centric electronics. Earlier navigation systems, such as the instrument navigation systems (VOR) used by aircraft, involved a lot of specialized electronics and still only provided the pilot with information about the plane’s angle relative to a ground-based transmitter. The pilot needed at least two of these systems and a set of good maps to figure out where the plane was.

A modern, GPS-based navigation system simply hands the pilot or driver complete information about where the plane or car is located. It does this using specialized input circuitry and specialized but very ordinary computer output circuitry (a display and sound system). Everything else is done by the microprocessor.

The input circuitry in a GPS receiver is interesting. The global positioning system consists of an array of earth-orbiting satellites that use microwaves to announce their locations and emit timing pulses. The navigation system’s circuitry detects those microwaves, determines the satellites locations, and uses the timing pulses to measure the distance to each satellite it can detect. Since microwaves travel at just under the speed of light through earth’s atmosphere, knowing how long it takes for a pulse to travel from a satellite to the navigation system is equivalent to measuring the distance separating those two objects.

Once the navigation system’s specialized electronics has received information about the satellites’ locations and measured the travel times of their pulses, that information is passed along to the microprocessor. The microprocessor does everything else. It converts pulse travel times into distances, uses those distances to triangulate the navigation system’s location relative to the satellites, looks up information about that location in its stored maps, and displays relevant information to the pilot or driver. Easy peasy.

The specialized circuitry necessary to receive location and timing information from the GPS satellites was once complicated and expensive. But the desire to put such circuitry in every cellphone propelled amazing miniaturization. The GPS receivers now built into cellphones are tiny and inexpensive, and they include their own microprocessors. Part of the microprocessor revolution has been that many devices contain entire networks of microprocessors rather than just one centralized microprocessor. Having many microprocessors that communicate via a network can save a lot of specialized wiring and it turns out that wires can be more expensive than microprocessors. Cars and planes now have communications networks that allow their many microprocessors to exchange information and control components with only a handful of wires.

How can an object spin at constant angular velocity when its parts are accelerating?

How can a spinning object keep constant velocity with the direction of its parts changing at every instant?

When you consider an object as rotating, you normally stop thinking of its parts as moving in their own independent ways and treat the whole assembly as a single object. While it’s true that the various parts of that object are accelerating in response to internal forces those parts exert on another, the object as a whole is doing a simpler motion: it’s rotating about some axis. This ability to focus on a simple motion in the midst of countless complicated motions is an example of the beautiful simplifications that physics allows in some cases.

When you push on a rotating object, when are you doing work?

When you push on a rotating object, when are you doing work?

That’s an interesting question and requires two answers. First, if you push on a part of the rotating object and that part moves a distance in the direction of the force you exert, then you do work on it. In principle, it is possible to identify all the work that you do on the rotating object via this approach.

However, it is also possible to determine the work you do entirely in terms of physical quantities of rotation. If you exert a torque on the rotating object and it rotates the an angle in the direction of your torque, you again do work on the object. That’s the rotational version of the work formula: whereas force time distance is the translational work formula, torque times angle is the rotational work formula.

An important complication arises, however, in that you must measure the angle in the appropriate units: radians. The radian is the natural unit of angle and is effectively dimensionless (no units after it). When you multiple the torque times the angle in radians, the resulting units are those of work and energy. If you use a non-natural unit of angle, such as the degree, then you’ll have to deal with presence of the angle unit in your result.

Rotating “up” or “down” — is that like clockwise and counter-clockwise?

When an object is rotating, both the “up” and “down” directions point along the vertical axis. Do they correspond to clockwise and counterclockwise?

Yes. Distinguishing between the two opposite directions of rotation using words alone requires that everyone agree on what to call those two directions. It also requires that everyone have an artifact that they can use to identify which direction is which. When something is spinning about a vertical axis, a carousel or merry-go-round, for example, then physicists name the two possible directions of rotation “up” and “down” and use a right-hand rule to identify which is which. Since most people have a right hand and know which hand it is, the necessary artifact is built-in.

In more common language, the two directions might be called “clockwise as viewed from above” and counter-clockwise as viewed from above”. In this case, the artifact is an old-fashioned analog clock and is probably more of a remembered artifact than one that is in the room with you. Nonetheless, that common naming convention is fine; it’s just wordier than the physicist’s version.

As a skater changes direction, is the skater accelerating?

When a skater changes direction, so that the skater’s velocity changes as a vector quantity, is the skater accelerating?

 Yes. Any change in a skater’s velocity involves an acceleration because acceleration is the change in velocity with time. So, if a skater is speeding up or slowing down, then it’s clear that the velocity changes because the speed part, the amount part a velocity, is changing. But when the skater’s velocity changes direction, so the skater is turning, even though the skater is traveling at the same speed, the skater is still undergoing acceleration and that acceleration still involves a net force on the skater, pushing the skater and bending the skater’s path.

What role does force play in a self-defense blow?

My self-defense instructor encouraged me hit the dummy with more force, so I exerted more force on my arm and it accelerated more rapidly. Yea for physics! But how does my increased force on my own arm cause me to hit the dummy with more force? — RL

Suppose you’re defending yourself against an attacker and you find that you have to hit them, either with your hand or with your fist. Two of the most important features of the impact between your hand and the person are how hard you push on the person and for how long.

The technical term for that push on the other person is a force; you exert a force on the other person. And a force is one of those physical quantities that has a direction to it. You can exert a force on someone toward the right or you can exert a force on someone toward left. Direction matters. Another thing about forces is that they’re always exerted between two thing, for example, you pushing on the other person. Forces don’t just exist by themselves; you can’t carry a force with you. You exert a force on something else.

That leaves this intuitive notion that you carry something with you during the wind up to an impact a little fuzzy. What is it you’re caring if you’re not carrying a force? Well, there is something you’re carrying: it’s known as momentum and momentum is a conserved physical quantity. That means you can’t create momentum or destroy momentum; all you can do is move it from one object to another.

In this respect momentum resembles money. Money is a conserved quantity, too, assuming that you don’t print it up in your basement (you are a law-abiding citizen) or you don’t destroy it (you’re not goofy). Money is conserved and goes from person to person to person. It is the conserved quantity of finance. Correspondingly, momentum is the conserved quantity of motion.

If you want to start moving to the right, you I have to accumulate some rightward momentum. Momentum, like force itself, has a direction to it. There’s momentum to the right; there’s momentum to the left. They are different, so if you want to move to the right, you have got to accumulate rightward momentum. The same is true of your hand or your fist, when you’re going after that attacker. If you want your fist to be really quick and move to the right rapidly, you have to invest a lot of rightward momentum into your fist.

To do that, you have to get that momentum from somewhere because you can’t make it. You can’t just cooking it up from nowhere. It comes from the ground and from the rest of your body. You pour rightward momentum—let’s suppose the bad guys are over to your right—you pour rightward momentum into your own fist. That momentum comes out of the rest of you and you do this how? By exerting a rightward force on your own fist.

You can do this—you can think of yourself as two separate parts: (1) your overall body and maybe your shoulder, and (2) the rest of you, your arm and your hand. So you’re pouring rightward momentum into your fist, at the expense of everything else. You actually can end up going backwards if you’re not careful

So you pour the rightward momentum into your hand and the amount of rightward momentum your hand accumulates is equal to the force you exert on your hand times the time over which you exert that force. The harder you push your hand and the longer you push your hand, the more rightward momentum it accumulates. If you want a fierce impact, You want to put a lot of rightward momentum into your hand. That means you push hard and you push long. You don’t go gently; you get going! You pour the momentum in so that its all accumulated.

This is this is the case not just for for punching somebody. It’s also the case for throwing a baseball. If you really want it to go fast, you need to take a long windup and you pour the rightward momentum into the baseball over as long a distance and with as much force as you can summon. Pack it full of rightward momentum, and off it goes. The same with a hammer. You pour rightward momentum into it, get it going and pack it full of momentum. When it hits the nail, its going to pack a wallop.

Okay, so now on to the impact. You have invested momentum in your hand; now when your hand hits something, it invests momentum in what it hits: the other guy, the bad guy. Your hand, which is chock-full of rightward momentum impacts that other person and transfers much or maybe even all its rightward momentum to that person by way of a force for a time. It’s passing along that momentum and it turns out that it can pass all of its momentum in a variety of different patterns. It can either pass along all its momentum with a gentle force over a long time, by pushing the person as they go away, or it can transfer all its momentum with a giant force for a short time.

If you hit knuckles to jaw, that impact is fierce and involves a big force, but not for very long. All the moment goes over in a jiffy. So a momentum transfer, it turns out, the amount of momentum you the put into something or transfer to something, is just this product of force times time. You can use a little force for a long time, or a big force for a short time; both of them can transfer the same momentum.

Well, if you really want to stun somebody, you want to make the transfer quick—short time, big force—and so that’s the bare-knuckle fight. It hurts. On the other hand, if you put on big fluffy gloves and delay or prolong the impact, it’s a little force for a big time. It more pushes you, but it doesn’t have that peak impact force that hurts.

So there you have it: if you’re trying to defend yourself against an attacker and you punch them, you do it by accumulating as much momentum toward the bad guy as possible. Use a big force for a big time, whatever you can do to get a lot of forward momentum into your knuckles and into hand. At the impact point—the moment when when you touch the other person—you want to transfer all that momentum to the other person, perhaps by way a big force for a short time. That’ll hurt everybody involved, you included, but, in any case, hopefully it will have the desired effect of getting the bad guy to go away and leave you alone.