In the classes I teach, a disconcerting number of students don’t really understand Newton’s third law of motion and get confused by the statement:

"For every action, there is an equal and opposite reaction."

In fact, the law would be more accurately expressed this way:

"For every force, there is an equal and opposite force."

Or, in mathematical terms:

"F1 on 2 = -F2 on 1"

For a book lying on a table (i.e., stationary), it is commonly thought that Newton’s 3rd Law is when the Normal Force and the weight of the book (m*g) cancel each other out and therefore the book goes nowhere. Actually, these two forces are not related by the Third Law. Given a (gravitational) force between the Earth and the book, the Third Law implies a force between the book and Earth, not the not the book and the table. Consider the math:

FG = G(MEarth)(Mbook)/ r^2

You usually learn that acceleration due to gravity, g, is

g = GMEarth/r^2

and the force due to gravity, aka weight, is mg. Newton’s 3rd Law states that the book must exert the same amount of force on the Earth… and it does!

acceleration (a) of due to the book = G(Mbook)/r^2.

Since in each case you’re using masses of the book and earth for accelerations, the forces come out the same when you multiply by the mass of the other body. Forces are masses * accelerations, which means you will arrive at the same force whether or not you’re using g or the acceleration due to the book. We’ve gotten used to just thinking about acceleration as g (which is immensely useful, no doubt), but it puts up blinders when thinking about forces, most notably weight.

Using the gravitational equation, you can figure out the force on the book due to the earth, as well as the force on the Earth due to the book. Each time, you will find the magnitude to be the same (although different directions). Using mg incorporates the mass of the book (or whatever) into the gravitational equation. Because of this, whenever you figure out the forces on the book or on the Earth, you end up using all the same variables. Try it out! This is what Newton meant by the Third Law.

-X

None. Or very close to none.

Time is of the essence on the Physical Sciences section; nearly everyone needs to finsh the section, but for most people that isn’t going to happen if they spend too much time reading unnecessary material. And it turns out that most of the text in physics passage is unnecessary for answering the questions.

When you first turn to a physics passage, it is fine to glance at the first few lines to see what it’s about, though even this isn’t necessary. What you must do is check out every picture, table, graph, and block-quoted (offset) equation. You have a particular task with each of these items:

• Pictures: Often these show an experimental setup, or the system being studied. Examine it to see what’s going on. If it’s confusing, do not spend too much time here; sometimes, you don’t really need to understand the entire experiment to answer all of the questions.
• Tables: These represent the most important part of many passages, because they show experimental results and AAMC loves experiments. For the moment (before you’ve read the questions), you have two tasks: (1) understand what the table is talking about, i.e., what experiment was performed — you may have to read a few lines of text above the table in order to do this; and (2) see what was measured — in other words, read and understand the column headings.
• Graphs: Do not analyze the graphs, just see what they are graphs of, by checking the labels on the axes and by reading a couple of lines of text above them if that’s necessary.
• Equations: Do not attempt to understand any equation that is offset from the rest of the text, but do see what it’s an equation for; again, this may necessitate reading a bit of text.

You then proceed to the questions, referring back to the pictures, tables, graphs, and equations as necessary.

About one question per passage, maybe not even that many, will require reading some more of the text, but by now you’ll have a good idea where to look and what you’re looking for, so you’ll be able to find it quickly. Many people worry about these questions, but they’re rarely a problem. If you have practiced enough passages and studied the right material, you’ll know immediately when they are asking you something that requires reference to the passage, because it’s not amazingly simple but it’s also not something that you saw in the pictures, tables, graphs, or equations. For such not-so-simple questions, look in the passage.

You might think it would make sense to read the passage first if you’re going to have to go back to it later. Not true. For one thing, some passages have no such questions. For another, for most test-takers reading the passage is a time sink. If you had the discipline to limit yourself to a quick skimming it would be fine, but under testing conditions most people hate to miss anything, so skimming becomes reading, and reading becomes time expiring before you’re done or having to spend insufficient time on questions to compensate.

This method will be uncomfortable at first, and maybe forever. To those who are still reading the passages because they feel more comfortable when they do that, ask yourself whether the discomfiture is actually costing you points, and whether the time lost is worth it. If you’re not 100 percent sure, test it both ways, but only after you’ve practiced the new method enough to get good at it. Remember, the point is getting questions right in the time allotted, not liking it.

This is everything you need to know about the Right Hand Rule (RHR), or rather the two versions thereof. One or the other of them applies any time you are finding a direction (whether of field, force, acceleration, or even something else), and charges are moving.

I detail the flat hand method — no sticking fingers in different directions perpendicular to each other.

There are two related right hand rules. Let’s say: Right Hand Rule 1 (RHR1) — used to determine the direction a charged particle, moving in a magnetic field, will be pushed; Right Hand Rule 2 (RHR2) — used to determine the direction of a magnetic field created by the movement of charges.

There are three parts of your hand to remember, and I try to make it is easy as possible:

1. Fingers = Field: stick your fingers (of your right hand) in the direction of the magnetic field; if you aren’t told the field (i.e., you are doing RHR2), the fingers are eventually going to tell you its direction. In other words, fingers = the first field you encounter in the problem. Remember, this is only for magnetic fields; electric fields have nothing to do with magnetism problems.
2. Thumb = hitchhike, in the direction of motion. Motion of what? Of the thing in the problem that’s moving (the charged particle or particles; if there’s just a current given, not particles, then that current would be the movement, by convention in the positive direction even though it’s usually the movement of negative particles in the opposite direction). In other words, the first motion you encounter in the problem. (Note: the direction it’s going now, not the direction of its acceleration.)
3. Palm = Push. Your palm will face in the direction that a positively-charged particle will be pushed by the magnetic field. For RHR1 problems, this is usually what the problem asked you to figure out. For RHR2 problems, it doesn’t really apply but it still works: a positively-charged particle moving in the same direction as the current will be pushed toward the wire by the magnetic field.

So, if asked to figure out the direction a particle is pushed, stick your fingers in the direction of the magnetic field, and hitchhike in the direction the particle is moving. Your palm is now trying to push the charge, in the appropriate direction. You just used RHR1.

If asked to make a magnetic field, hitchhike in the direction of the moving charges (or the current); your fingers, which now are allowed to curl, show the direction of the field, which curls around the path of the charges. You just used RHR2.

Related issues:

• The magnetic field does zero work, always. This is because it is always perpendicular to motion, turning the particle rather than speeding it up or slowing it down. That’s why we can kind of throw it in there at the end of electrostatics: it has no effect on the energy of anything.
• It is possible to use the analogous left hand rule to solve problems for negative charges moving in magnetic fields, but I recommend against it. Use RHR, of whichever type, and for negative charges or currents the answer is the opposite direction.
• Electric fields do not create magnetic fields; these two are unrelated for your purposes. You’ll know this if you try to apply RHR inappropriately — you can’t stick your fingers in two different directions.

On the MCAT:

• Ropes, cables, wires, and strings are just ways to apply forces (except when they’re vibrating…).
• The force on a rope etc. is always applied along the line of the rope, and it is the same in both directions. It is equal to, by definition, the tension on the rope.
• The amount of force, i.e., the tension, is the same throughout the rope. In particular, it is the same on each side of a pulley.