# Is Newton's First Law an actual law, or just the definition of force? [duplicate]

Newton's first law, as you all know it, states:

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

Now what is force? To me force means action by which the velocity of an object changes. Now following this definition of force First Law doesn't seem any law.

It is just like saying that; If in a world where there are no mangoes, in that world there can't be any mango juice. When I/we say that "If their were no force" , it means that "If there were no things/action to change our motion". So clearly in such world where there is no force/friction then there can't be any thing which can "change our motion". So that implies that object will continue to be in uniform motion . You can see that first law is not a law, but is mere an implication from a trivial definition of force. So why then first law is a law?

• Your definition of force is exactly the second law of Newton. Jan 8 '20 at 13:08
• This answer to this question elaborates what newton's laws really mean. And your question is duplicate of this question.
– user249968
Jan 8 '20 at 13:13
• Does this answer your question? Are Newton's 1st and 3rd laws just consequences of the 2nd?
– user249968
Jan 8 '20 at 13:14
• Have a look at physics.stackexchange.com/q/70186 . Then if the si something which is not convincing or you ned additional clarification you may ask a new question. Jan 8 '20 at 13:15
• @GioegioP Answers of this question are too technical for me. I am a high school student and terminology of these questions are over my head.
– user251214
Jan 8 '20 at 13:22

## 6 Answers

Now what is force? To me force means action by which the velocity of an object changes.

A force may be considered to be any influence which tends to change the motion of an object. I emphasize "tends" because a force does not necessarily change the motion of an object if the net external force on the object is zero.

Now following this definition of force First Law doesn't seem any law.

Newton's first law can be viewed as a statement about the inertia of an object, that an object will remain in its current state of motion unless there is a net external force that changes its motion, i.e., the gives it an acceleration. Newton's second law tells us that an object will undergo a change in motion (acceleration) only if subjected to a net external force. That doesn't mean the object is not subjected to forces.

Putting the two together, one can consider Newton's first law as a special case of the second law, that is, the case where the net external force on an object is zero.

So clearly in such world where there is no force/friction then there can't be any thing which can "change our motion". So that implies that object will continue to be in uniform motion .

That would be correct if there is no net force force on the object. You can have external forces acting on an object without a change in motion of the object if the net external force is zero.

You can see that first law is not a law, but is mere an implication from a trivial definition of force. So why then first law is a law?

It is not "merely an implication from a trivial definition of force". As I indicated above, the first law can be considered as a special case of the second law. And the second law says that an object will not change its motion unless acted upon by a net external force.

Hope this helps.

Actually the action of a force does not necessarily need to make an object change its velocity. Here's an example:

Consider a block over a surface with a really high static friction coefficient $$\mu$$. Now, if you apply a force $$F$$ that is less than the frictional force involved, you won't be able to change it's velocity even though you are applying a force. The concept of force is way different from just being the action that makes the velocity of an object change.

I can't help that it's such a philosophic and definition kind of thing when we talk about laws. By the way, I prefer the First Law statement as the one below:

An object has constant velocity if, and only if, the net force submitted is null.

When we say it has constant velocity it already tells us about the rest state or the rectilinear motion state.

To what concern the definition of force, I believe a better definition would be:

Force is a strength or energy as an attribute of physical action, which may or may not change the motion state of a system.

Moreover, the applications of the First Law are not limited to its own statement. It is also used to define what is called inertial and non-inertial reference frames, which would be way more difficult to explain only using the definition of force.

In short Newton's first law states that there exists a reference frame (called inertial reference frame) in which the Newton's laws are valid and the second law (building up on Newton's first law) states that in such a reference frame $$F_{net}=m a_{COM}$$.

COM:Centre Of Mass

A force in classical physics is either gravity or Lorenz force or some macroscopic" pseudo force" which when broken down to more fundamental parts is either of the two. For example drag is a force given by - cV vhere V is the velocity vector. Newton's second law gives you the differential equation of motion relating forces to the changes in momentum : The second time derivative of momentum of a point like body is equal to the sum of the forces on that body.

So according to you, there can be a condition where there is no force. But this not possible in reality. There is no such body which experiences zero force on it. A body always experiences net zero force if all the acting forces get to cancel out. Now imagine you are standing on earth, how you are stable? Stable means no force. But there are tonnes of forces acting on us while only standing on-earth. But the net force is zero. That's why you are in a stable position while standing. Hope this works!

Newton's First Law is not defined the way you have put up. The definition you have shown is a school level definition. The more precise definition comes at the graduation level, which is as follows:

If the net force on a body is zero, then in the frame of this body, it is possible to choose a reference frame which is either at rest or in uniform motion, such a reference frame is defined as "Inertial Reference Frame".

And, the reference frame which is not at rest or in uniform motion, w.r.t. a body on which the net force is zero, is called a "Non-Inertial Reference Frame".

Newton's First Law actually defines the condition in which Newton's Laws would be applicable, which is "Inertial Reference Frame" in this case. Newton's Laws are applicable only in inertial reference frames, they are not applicable in Non-Inertial Reference frames.

Now, let's come back to your question.

Now what is force? To me force means action by which the velocity of an object changes.

This is right.

The problem comes when we take the definition of Newton's First Law as you have proposed. In that case, it seems like a Tautology, and you are right in saying that.

When we take the definition I mentioned, then it makes more sense.

I am assuming that you know that Newton's Laws of Motion are not applicable in Non-Inertial Reference Frames, so when we define them, we first have to define the condition under which they would be applicable and Newton's First Law is essentially the condition under which the other laws would be applicable.

If we take your definition of First Law then it seems like an implication of second law itself, which is not true. Science would never put the same thing twice in different languages.