Whether we’re on the bus, the tram, or the tube, we all dread being thrown backwards into the lap of an unsuspecting stranger when the thing starts moving before you’ve found a seat. But why do we get thrown backwards anyway? Aren’t we moving forwards? If you’ve ever found yourself meekly apologising to a fellow passenger and thinking “Why did THIS have to happen!?” then read on, because it can all be explained by Newton’s 1st Law.
Isaac Newton (yes, that Isaac Newton) probably never fell over on a bus, but that didn’t stop him from formulating his three laws of motion, which he published in his Philosophiæ Naturalis Principia Mathematica in 1687. As you might guess from the title, the book was published in Latin, not English (and almost didn’t get published at all), but if your Latin happens to be a little rusty, a rough translation of the 1st law reads as follows:
“Every body perseveres in its state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change its state by forces impressed.”
Euh. Are we sure that’s in English? Let’s break it down a bit.
“Every body…”
Okay, let’s stop there a sec. What even is a ‘body’ here? The word body could be used to refer literally to someone’s body (and in the case of you on the bus, it’s referring to yours!), but more generally it’s just a fancy word for object. Newton states that the law applies to every object, which makes sense, as being true for all objects is what makes something a law in the first place!
“…perseveres in its state…”
Here, Newton is saying that whatever the object is currently doing (its ‘state’), it will continue to do so (it will ‘persevere’).
“…of being at rest or of moving uniformly straight forward…”
But what is the object currently doing? Well, it’s either ‘at rest’ or ‘moving’, right? This is why you’ll often hear the 1st law simplified as “Things in motion stay in motion; things at rest stay at rest”. But that simplification misses out some crucial parts of the first law! For a start, what kind of motion are we talking about here? After all, an object could be ‘in motion’ at any number of different speeds, but we wouldn’t expect to see it suddenly speed up all by itself! Luckily, the first law is actually a bit more specific about this – it specifies that we’re talking about objects that are ‘moving uniformly’, meaning that they’re moving at a constant velocity. This rules out the possibility that our object could suddenly start moving at a different speed, because that would involve a change in velocity, also called an acceleration (confused about the difference between speed and velocity? See our article on vectors).
Speaking of velocity, an object at rest is actually moving at a constant velocity as well – a velocity of zero! So, if we wanted to simplify the 1st law properly, we could say that “All objects stay moving at a constant velocity”, and we’re done!
…Except we’re not. The world would be a very boring place if everything just moved at the same speed all the time! What does the 1st law say about that?
“…except insofar as it is compelled to change its state by forces impressed.”
The last part of the law explains the circumstances under which an object would stop moving at a constant velocity, i.e. ‘change its state’, or accelerate. It says that this happens when a force is ‘impressed’, or applied, to an object, so full simplification of the 1st law might read something like:
“All objects stay moving at a constant velocity, unless a force is applied.”
Great! But wait, are we sure this is right? Surely if this were true, you could accelerate your car to 40mph, then turn off the engine and rely on Newton’s 1st Law to keep you travelling at that speed for the rest of the journey! I can see the ads for compensation claims already: “Have you been wasting thousands on unnecessary fuel usage?…”
Unfortunately (or perhaps fortunately?) for us, the 1st law doesn’t actually predict this. In everyday conversation, an acceleration usually means speeding up, but in physics, we use it to mean any change in velocity, and that includes slowing down as well! In a car, your engine provides a force that gives you a positive acceleration, but there’s also lots of external forces, like friction and air resistance, that work against you to slow you down. If you turned the engine off, these forces would quickly slow you down to a stop. We can still observe that the constant velocity prediction of the 1st law is correct, though, by looking at motion in places where there are very few resistive forces, like in space! Once we’ve launched a rocket into space and it’s burned up all its fuel, it really will just keep travelling forever at whatever velocity it happened to be at!
Ok, it makes sense that forces working against you make you slow down to zero, but something still seems off, doesn’t it? Why do we need external forces to do that anyway!? In the absence of any forces, shouldn’t we just slow down to zero regardless? Why should constant velocity be the steady state; wouldn’t slowing down to zero require less effort?
Well, the thing is that, perhaps counterintuitively, we actually can’t tell the difference between an object moving at a constant velocity greater than zero and one moving at exactly zero. Remember earlier when we emphasised that objects at rest are moving at constant velocity as well? That’s because they’re the same thing.
What!? But that doesn’t make any sense! Of course they’re not the same thing! Otherwise, how would we measure velocity at all? “Sorry officer, I wasn’t really speeding, because, you see, I was actually moving at a velocity of zero…”
The answer is that, when we measure velocity, we always have to measure it relative to something else. On Earth, we generally measure the velocity of an object relative to the Earth’s surface, but this is only for our own convenience. We could measure it relative to anything, really. This is why you can be ‘standing still’ on the Earth’s surface and yet still be moving at thousands of miles per hour due to the Earth’s movement around the sun. Are you moving at 0mph or 67,000? Depends what you’re measuring against!
This actually comes in handy when it’s time to think about you falling over on the bus! Let’s see if we can piece together why it happens:
- When you get on the bus, you and the bus are both at rest (moving at a constant velocity of zero) relative to the ground
- When the bus accelerates, it applies a force in the forwards direction to the parts of you touching the bus, causing you to change your velocity, or accelerate, in that direction
- However, this force isn’t applied to your entire body at the same time! It’s your feet that are touching the bus, so they’re going to experience the acceleration first, then pull the rest of you along later!
- Because your upper body hasn’t yet had a force applied to it, it’s going to remain at rest relative to the ground – relative to the bus, however, it will actually seem like your top half is getting pushed backwards!
- This gives us two ways to look at why you fall over – to somebody outside the bus, it looks like your feet get pulled out from underneath you, causing you to topple backwards. To you on the bus, however, it feels like your feet stay where they are and some force pushes your upper body backwards!
Of course, there actually is no force pushing you backwards. The only real force is the one the bus exerts on your feet, and that’s pulling them forwards. The force you feel pushing you back is a fictitious force, meaning that you only experience it because of your point of view, or frame of reference. The fictitious force here is caused by the physics of the 1st law, as it’s experienced due to the tendency for the velocity of an object to remain unchanged, or inert, in the absence of a force. This is why the 1st law is also known as The Principle of Inertia.
For future reference, whenever we refer to something as being inertial, we mean that it’s non-accelerating (this might come in handy later!). But what about when an object does accelerate? How do we know the amount of acceleration we’ll get from applying a force? Luckily, Newton explains it all, using his 2nd Law of Motion.