CONCEPTUAL PHYSICS › CHAPTER 2, NEWTON’S FIRST LAW
Why Things Keep Going, and What It Takes to Stop Them
For two thousand years the obvious answer was that motion needs a cause, and that anything left alone comes to rest. It is the answer your own experience gives you every day. This chapter is about why the obvious answer is wrong, and what had to be noticed before anyone could see it.
2.A State Newton’s first law and say what it claims about an object that is already moving.
2.B Explain how Galileo’s ramps make the case for inertia, and why no single experiment could ever show it directly.
2.C Tell mass from weight, and say which of the two measures inertia.
1. The answer everybody starts with
Push a book across a table and it stops. Stop pedaling and the bicycle slows. Let go of a trolley and it comes to rest. From that, one conclusion is almost impossible to resist: motion needs a cause, and rest is what things do when nothing is acting on them.
Aristotle thought so, and he was not being stupid. Nothing in ordinary life contradicts it. The idea survived for two thousand years because it fits every experiment you can do in a room with friction in it, which until Galileo was every experiment anyone had done.
2. Galileo takes the friction out
Galileo could not build a frictionless surface, so he did something better: he built a situation where friction could be made smaller and smaller, and watched which way the answer was heading.
Roll a ball down one ramp and up another and it climbs back to nearly the height it started from. Polish the ramps and it gets closer. Now lower the second ramp. The ball still climbs to the same height, so it has to travel further along the ramp to get there. Lower it again and it travels further still.
The ball is always released from the same height on the left. Lower the second ramp with the slider and watch two numbers: the height it reaches, which does not budge, and the distance it has to travel to get there, which grows without any sign of stopping.
Now ask the question Galileo asked. What if the second ramp were flat? The ball is still trying to reach its original height, and on a flat surface it never can. So it never stops. Not because anything is pushing it along, but because nothing is stopping it.
Notice what kind of argument that is. Nobody ever ran the flat case, because nobody could. The conclusion comes from watching a trend and following it to its limit, and it is one of the most important arguments in the history of science.
3. Newton’s first law
Newton wrote it down as a law about two situations at once. An object at rest stays at rest, and an object in motion keeps moving in a straight line at a steady speed, unless a force acts on it.
Read the second half again, because it is the half that is strange. Continuing to move is not something that needs explaining. It is the free option, the thing that happens when nothing interferes. What needs explaining is any change: speeding up, slowing down, or turning.
4. A tablecloth, and why speed is the whole trick
The dishes on a tablecloth are not glued to it. When you pull the cloth, friction drags them along, and given long enough they will come with it. The trick is to make sure there is not long enough.
Pull slowly and friction has a second or more to work on the dishes, which is plenty. Pull fast and the cloth is gone in a twentieth of a second, so friction gets almost no time and the dishes barely move. Their inertia does the rest.
Set how fast you pull and let go. The friction force on the dish is the same in every case, because the dish and the cloth have not changed. The only thing you are changing is how long that force gets to act.
The demonstration is often described as being about the force being small, and it is not. The force is the same at every speed on that slider. It is the time that changes, and a force that acts for almost no time produces almost no change in motion.
5. Mass is the measure of inertia, and weight is not
Two things are easy to confuse here. Mass is how much matter there is, and it is what makes something hard to get moving or hard to stop. Weight is the pull of gravity on that matter, and it depends on where you are.
Take an anvil to the Moon and its weight drops to a sixth. Its mass does not change at all, and neither does the trouble you will have stopping it if somebody rolls it at you. An astronaut can lift it easily and would still be badly hurt by a moving one. That is inertia, and gravity has nothing to do with it.
This is also why a large ship takes miles to stop, and why it is harder to shake a full backpack than an empty one even while you are holding both off the ground. In every case what you are up against is the amount of matter, not its weight.
Check yourself
1. A hockey puck slides across smooth ice at a steady speed. What is the forward force pushing it along?
There is not one, and it does not need one. Nothing has to push it to keep it going; the puck keeps going because nothing much is stopping it. The only reason the question feels like it needs an answer is the Aristotelian habit from section 1.
2. Galileo never rolled a ball along a genuinely frictionless surface, and neither has anyone since. How can the law be built on an experiment nobody has ever done?
Because the experiment that was done shows a trend. As the second ramp is lowered, the distance grows, and it grows without ever showing a sign of leveling off. The law is the limit that trend is heading toward. It is an argument about the shape of a whole set of results rather than a reading from any one of them, and it is much stronger than a single measurement could be.
3. Explain the tablecloth trick without using the word inertia, then again in one sentence with it.
Without: friction from the cloth pushes the dishes sideways, but the cloth is only under them for a very short time, so that push has almost no time to change how the dishes are moving. With: the dishes have enough inertia that a brief friction force cannot change their state of motion appreciably. Both are the same sentence, and the first one is the one that explains anything.
4. An astronaut on the Moon can lift an anvil with one hand. Would being hit by one rolling toward her at walking pace be any gentler than on Earth?
No. Lifting it is a question of weight, which has fallen to a sixth. Stopping it is a question of mass, which has not changed at all. The anvil is exactly as hard to stop on the Moon as it is here, which is the cleanest way to see that mass and weight are two different things.
5. You are standing on a bus that brakes hard, and you pitch forward. A classmate says a force threw you forward. What is wrong with that, and what actually happened?
No forward force acted on you at all. The bus slowed down and you did not, because nothing had yet slowed you; you carried on at the speed you already had, which from inside the bus looks like being thrown toward the front. What finally stops you is the floor, a handrail, or the person in front, and those are the only forward-facing forces in the story.
Chapter 3, Linear Motion. This chapter said that changes in motion are the thing worth explaining. The next one builds the vocabulary for describing those changes precisely, which is what the rest of the mechanics in this course is written in.