That which you think of as "at rest" is actually in motion. That glass on the coffee table is moving at 1000 km/hr as the earth rotates (relative to the center of the earth and depending on your latitude). Everything on earth is moving at 30,000 m/s relative to the sun... etc.

Only change in motion requires an external force, otherwise, everything just cruises along.

Absence drag forces like air resistance an object can travel at constant velocity without any added force. It in fact it will take a force to slow it. Velocity is stored energy, but it doesn’t cost energy to keep moving (again absence drag forces). Think of something flying in space.

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Layman here - could we not use your definition and combine the first 2 of Newtons laws? Ie - was Newton making the same mistake as op thinking he was in a static frame of reference?

I'm not sure what you're thinking, but the key difference between Newton's first law and Newton's second law is that Newton's first law tells you that inertia exists, and Newton's second law tells you how much momentum of an object changes when you exert a force on the object. They're not equivalent.

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An object with nonzero velocity has kinetic energy, potential energy normally is due to the position of one object relative to others.

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Well, the way Newton laws are thought in US schools is weird, and it creates a lot of confusion. The original newtons laws are ais they thought in schools, but nobody teaches the Scholium that precedes the laws.

In the Scholium Newton talks about absolute and relative motion. He mentions absolute coordinate frame, defined by immovable stars. Other frames are relative. Newton says that you cannot really distinguish two relative motions when forces are not actet on two objects. But if you connect these objects be a string and make them spin, by observing the tension of the string you can distinguish that spinning motion.

What Newton actually talks about in the Scholium is about inertial frames of reference, and all other laws can be applied only in such frames (actually Newton thinks that there is one true non-moving frame of reference).

These definitions in Scholium and explanation when we can replace absolute motion with relative motion is quite important. So in some other textbooks they are included as the first Newtons law, which is condensed to "all mechanical processes in inertial frames flow the same", or that "all inertial frames are indistinguishable". This definition of inertial frames may sound confusing at first, but it makes a lot of sense the more you think about motion and general applicability of Newton's laws. You can think about inertial frames as frames that stay in rest or move with constant velocity relative to each other.

This is exactly why Newton's laws were revolutionary and why it took humanity until 1687 to discover them! Until then, it was perfectly reasonable to believe everything naturally slows down and stops, unless someone is working hard to keep it moving. That's because everything we could see around us did just that! We know now that everything that we see slowing down does so because of friction and air resistance, but it was not obvious if you've never seen anything different. It took Galileo's physics experiments with carefully constructed artificial conditions to inspire an alternate explanation.

Maybe the closest everyday example of a self-moving object they had at the time was a runaway horse cart. Later on it was an easier idea to swallow when we had trains around. Trains have such low friction that you have to work hard to slow them down. It's more natural to believe that an object in motion remains in motion if you've seen trains your whole life!

thanks for the response! I get that friction and opposite forces causes objects like the skateboard to decelerate, but how is it that the object itself can keep going forward at constant velocity? I am just wondering what causes the object to keep moving if there is no net forces acting on it? Is that part of inertia something we just have to accept is true?

Another example, if I push a box on a table with a constant velocity, the friction force is equal to my applied force, but since they are both equal it makes intuitive sense that net force = 0 = no movement at all. How is it that the object can till move with no net force?

>object can travel at constant velocity without any added force. It in fact it will take a force to slow it.

I understand that the forces acting on the object opposite of its motions causes it to decelerate. With your space example, I know if you give something an initial push, it will keep moving forever unless another net force acts on it. But how does it keep moving forward? I know that something must act on the object for it to change acceleration, but how can it move in the first place without any net force. It intuitively makes sense to me that when net force = 0, then that means no motion, but how can an object move at all when net force =0? Is that just inertia by definition?

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Thanks for the reply, and sorry if my original question was unclear.

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Yes, but why does only change in motion require external force, and not the motion itself? How can an object like Earth just move in space with constant tangential velocity? Intuitively, it makes more sense to me that something is exerting force on the earth to make it move at all. If I throw a ball in space, I know my hand exerts force on the ball for it to accelerate, but when I let go, it will keep moving forever in a straight path, with no force acting on it. How is that?

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Also, when I push a box on a table at constant velocity, my applied force is equal to the friction force. The net force is 0, but how can the box move? It intuitively makes sense to me that net force = 0 = no movement. I know the answer to this question is inertia, but I don't know this property of matter confuses me. Do I just need to accept this as a fact?

But what keeps the train moving? I know the answer to this question is inertia, but intuitively it makes sense that there must be some force that is making the object continue to move, even at a constant velocity. I guess a better question is do we know why objects with no net force can remain in motion? Like, it makes sense to me that when net force = 0 = no net movement, but not the constant velocity part.

Force changes acceleration. So you need a force to accelerate an object from rest to a constant velocity. But at a constant velocity acceleration is zero and so is the force. There in energy in the object, energy from the initial force used to accelerate it, but it doesn't cost energy to keep moving.

For every action there is an equal and opposite reaction. Basically gravity is the external force which can (and does) change the motion of an object; recall ‘gravitational constant’.

Your problem is that you are too much tied to your experience that tells you that you need force to keep something moving. But that was the ingenious approach by Newton to figure out what would happen if there is a single object in vacuum that does not interact with anything.

Your question with pushing an object is related to Newton 3. You, in fact, apply a force on the object that results in a force from the object to you. Since you are much heavier and you also can use additional force to keep you at rest, you will more or less stay in position. The object will then act with a force on the table. If not compensated by other forces such as friction on the ground, this results in the table to move. The same force acts back on the object, but with opposite direction. If the net forces acting on your object (your initial force and the force from the table on the object) do not balance, this results in an acceleration following Newton 2 (F=ma).

Note that at rest, the friction is much stronger. You have to apply a larger force to commence with moving the box, while you need much less force to keep it moving at constant velocity. The reason is the smaller friction of gliding objects.

By the way, box on a table is already quite complex. Consider instead a car at rest. In order to accelerate, the car acts via the wheels with a force on the earth in the opposite direction of where you want to go. To move forward, the force is backward, and vice versa. The earth acts with the same force on your car, but in the opposite direction. This pushes your car in the desired direction. In principle, earth gets accelerated, too, but this is negligible due to the ratio of masses.

Finally, I would like to add that Newton 1 yields a definition of a distinct class of reference frames. They do not rotate or accelerate with respect to each other, and all yield that an object is either at rest or moving with constant velocity in the absence of forces. Our earth is not such a frame, even in the absence of gravity, because it is rotating.

Consider energy. When you throw the ball in space, you give it kinetic energy (m*v^2/2) now unless an other force is applied on the ball at some point, this energy has no reason to disappear. It will not fade nor change. So it will keep moving forever.

On earth though, you throw the ball applying kinetic energy, but it also has potential energy (made by gravity as mgh) and air will apply friction energy opposite to the movement vector(proportional to f*v). As energy is conserved, it does not disappear, it will switch from kinetic to potential and inversely. Friction and hits will turn to thermal energy.

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Look at it from a different perspective. Why should you assume an object will slow down? The main concept we use to describe an object’s motion is position. We call the rate of change(slope) of position velocity, and we call the rate of change of velocity acceleration. Suppose an object starts at v=0, and we apply a constant force on it to accelerate the object to v=10. So on a graph this looks like a line linearly increasing to 10 and then going straight. Now, if you assume you need a force to increase the velocity up to 10, why wouldn’t you need a force to decrease it? Starting at zero vs starting at v=10 will both be straight lines on a graph. The only way to change velocity is to accelerate it, which requires a force.

Just in case you are confusing velocity with acceleration (very common mistake). Net force = 0 simply means that the object is not changing in velocity. Force is defined as ma, so if f=a=0, there is 0 change in velocity. The problem isn’t that there’s something causing it to keep moving, it’s that nothing is stopping it from moving. You must have a force to change the velocity of an object. Also, all velocity is relative. You could say you’re going 10 m/s. But you could also say everything around you is going at -10 m/s, and you’re going at 0. So how do you stop? You slow down by applying a force so that you move at -10 m/s like everyone else. My point is, velocity being zero is just a convenient starting point, it holds no actual significance because we only care about its change. Whether something is moving or not moving is actually the exact same state. Your velocity is zero on a plane, even though you’re moving. Your velocity is zero on the earth, even though you’re on a rotating object.

Edit: To answer your question: assume the box is moving with some constant velocity v. There must be a net force to change it. That’s it. Force can only affect acceleration, or rate of change of velocity.

The biggest idea to give up is that there is an absolute state of rest. There is no universal stationary or rest state. You can only measure velocity relative to something else. By convention, we measure velocity for many things relative to the surface of the earth because that’s where we exist. We require constant energy to walk forward because we have to push against gravity each step. Cars and trains require constant energy to move forward because of things like friction/drag. In a vacuum (ie space), there is nothing to stop an object from moving. So once it’s set in motion, it will continue in that state until something changes it. But remember again that there is no standard motionless point in the universe. Everything is technically in motion and at rest at the same time depending on how you measure it. We measure a car’s speed relative to the surface of the earth but the surface of the earth is spinning very quickly. The earth itself is moving very quickly around the sun. And the sun is moving very quickly around the center of the galaxy.

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I read almost all your replies Kwooosh, the keyword you are using is "intuitively". The problem is that since we lived our whole life on earth where friction happens all the time this make sense for this topic to feel counter-intuitive. Newton law is a mathematical model and it could be counter-intuitive sometimes.

You're confused because you think "at rest" and "in motion" are different things, but they're not. They're the same.

Imagine two space ships, Firefly and Enterprise, in deep space set on a collision course. The captain of the Enterprise radios the captain of the Firefly saying, "Firefly, you're moving towards us at 1000m/s. Please engage reverse thrusters to match our velocity or alter your course." The captain of the Firefly responds, "No, Enterprise. YOU'RE moving towards US at 1000m/s. You engage YOUR reverse thrusters or alter YOUR course."

Who is right? Both, and neither. Both are correct from their own inertial reference frame, and both are incorrect from the other's inertial reference frame.

Yes, that is just inertia by definition (see below definition from dictionary.com) "the property of matter by which it retains its state of rest or its velocity along a straight line so long as it is not acted upon by an external force."

>But what keeps the train moving? I know the answer to this question is inertia, but intuitively it makes sense that there must be some force that is making the object continue to move, even at a constant velocity. I guess a better question is do we know why objects with no net force can remain in motion? Like, it makes sense to me that when net force = 0 = no net movement, but not the constant velocity part.

Why is it that when you're standing inside a train (or airplane or car) moving at constant speed, you move along with the train without having to constantly horizontally push on the floor?

According to your reasoning, you're moving at constant velocity and that means you need to be pushing on something to keep moving forward. But actually you don't have to push on anything. Does that tell you anything about your intuition with respect to motion in different frames of reference?

You may also want to contrast this experience with your experience on something like a merry-go-round, where you know that unless you are actively exerting force against a pole or something else on the merry-go-round, you'll fall off. Do you know what the key difference between these situations is?

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Yes you need to just accept it as fact.

The view that you have is a common misconception because in our daily lives, we’re surrounded by invisible forces that make it appear as though objects stop moving when we aren’t interacting with them. The common sense explanation is that the universe works as your describing. Fortunately, through rigorous science, we can discover the true (or closer to truth) laws of the universe by controlled experimentation and reproducible measurements that hedge against our inherent biases.

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Here on earth, things are continuously affected by the force of gravity and friction (air resistance, water resistance, rubbing against a solid surface, etc.) To keep something moving here in earth, therefore, you have to continuously apply force to counteract those ever-present forces. That’s why it seems so natural for things to be that way.

In the absence of gravity, friction, and any other forces, however, an object will continue to move in the same direction and at the same speed until a force is applied. In fact, it would actually require some sort of force to make it slow down to a stop.

I don’t know how much science fiction you may have read, but there’s a fairly standard theme with sub-lightspeed spacecraft voyaging from earth to nearby stars. They constantly accelerate and build up speed until they’re at the halfway point, then they flip around and accelerate in the opposite direction in order to slow down enough to stop when they arrive. If they simply accelerated in the same direction the entire time, they would overshoot their destination with no way to stop.

Hope this helps!

I like the energy response. A lot of things make more sense when you look at them from that perspective. Quite simply put: things move through the universe on a path of constant energy. A moving object has a certain amount of kinetic energy and will continue moving in a way that exactly preserves that energy, unless some force is applied to it.

You know how the path of light can bend in the presence of a black hole or other massive object. I’ve heard a lot of explanations for why this happens, and one is that the light follows the path of zero change in energy. Like contour lines on a map showing elevation.

Hope this helps!

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Velocity is relative. That includes a velocity of zero. There's no such thing as being "at rest" in an absolute sense. Right now you consider yourself at rest, but to the billions of neutrinos passing through your body every second you're travelling at nearly the speed of light! So the idea that things at rest stay at rest is the same idea that things moving with a constant velocity maintain their velocity. If they don't feel like the same idea, then you haven't yet come to a full appreciation of the principle of (Galilean) relativity.

The reason that it's hard at first to wrap your mind around the principle of relativity is that the forces due to gravity and friction dominate our lives. In our everyday experience, there's very much a difference between being at rest and moving with respect to the air, nothing we push keeps moving in a straight line forever at a constant speed, and everything that goes up comes down. Coming to terms with Newton's 1st Law requires understanding that we're surrounded by complex "special cases" that hide the underlying simplicity of inertia. It's not intuitive, but you can build up an intuition here.

On force...

While force is related to phenomena you're familiar with (e.g., pushing and pulling), ultimately it's an abstract quantity, and it's simply a fact that (net) force is directly proportional to acceleration, not velocity. If it helps, you can regard Newton's 2nd law as a definition: the net force acting on a body is defined as the body's acceleration scaled by its mass.

Also, don't confuse the net force acting on an object with any particular force acting on it. When you push the box and it moves at a constant velocity, it has no net force, but you are still applying a force to it. Think of it like this: the table is trying to bring the box to rest, and you're applying the force that's preventing that from happening. As soon as you stop pushing, the only remaining force acting on the box is due to friction with the table, and since the net force is now not zero, the box's velocity changes as it slows to a stop.

You've had lots of good discussions and good replies here, but it's still not clear if you're on board with this now(?).

I'll have crack but taking a wider view.

Newton came up with these laws to try to explain observations he'd made of the world around him.

He came up with words like mass, force, acceleration, momentum and then came up with some mathematical relations between them. These 'laws' allowed him to make predictions about the universe that were accurate.

Given that they were accurate, they were also useful! Hence they've been widely adopted.

None of us created the universe, none of us have a perfect understanding of how it works. Whatever is causing our universe to tick forward might not be using Newtonian dynamics at all.

There is no experiment we can do to prove that mass or forces exist. We can make observations that are consistent with Newtonian dynamics, but that doesn't make it universal.

In fact we know for a fact at astronomical length scales it isn't, because Newtonian dynamics makes incorrect predictions about the momvment of stars etc. (hello general relativity!).

We do, however, know these laws are often very useful at day-to-day length-scales.

So you can have your own theory that an object in motion tends to slow down, or requires something 'a force' to keep it in motion. But if you do, then you need to explain why satellites don't slow down in space and drop out of the sky. You need to explain why when I'm in my car on the motor-way, I don't feel the seat pressing into my back when I'm at constant speed.

On the flip side, your contention with Newtonian dynamics is that you have observed that objects in motion tend to slow down. Newtonian dynamics has an answer to that - in all these cases, there is an external force acting on the objects slowing them e.g. friction or wind resistance.

For me Newtonian dynamics, seems to provide a more complete picture of the world and does a better job explaining my observations. So, for now, I'm going to stick with using those rules to make predictions in my day-to-day.

Of course, it's a bit unintuitive this idea that objects at motion continue at motion... that's why Newton is widely considered to be a really really smart guy. He managed to get his head around that idea and ended up with a theory that made so many accurate predictions.

For some reason objects remember their state of motion. This is what Newton's first law says. We do not know why this is the case, just that it is. It is an unsolved puzzle. So either accept it or solve it.

>If I throw a ball in space, I know my hand exerts force on the ball for it to accelerate, but when I let go, it will keep moving forever in a straight path, with no force acting on it. How is that?

Why did the ball start moving?

You exerted force on it.

What would cause the ball stop moving, or otherwise change it's motion?

An external force acting on it, like someone catching it.

Why does the ball move in a straight line with constant speed?

>No force acting on it.