# Are Newton's 1st and 2nd laws equivalent statments?

it looks like that if F=0 in Newton's second law then the acceleration will be zero and this is the same statment of the first law-- the body will remain in rest or constant speed.
they are not equivalet I know, I am not smarter than Issac Newton , but why I am wrong?

ZapperZ
Staff Emeritus
Er... why do you think you're wrong?

Newton's 1st Law is a SPECIAL CASE of Newton's 2nd Law, i.e. you get Newton's 1st Law when F=0, just like you said.

So what is wrong here?

In fact, all three laws are essentially a manifestation of the same thing. They are not different from each other.

Zz.

Tide
Homework Helper
The first law describes a property of matter (i.e. its state of motion cannot change unless acted upon by something and that something is called a force) while the second law specifies how that change occurs (i.e., acceleration is proportional to the force). It's a bit circular to state that the first is a subset of the second since the first is a prerequsite for the second.

I dont feel good about it. I even read that Newton himself stated that the explanation of nature must be made using a minimun number of principles. and I think that's what should be because if they were equivalent so nothing prevents me from making them four laws or five... Vereinsamt said:
it looks like that if F=0 in Newton's second law then the acceleration will be zero and this is the same statment of the first law-- the body will remain in rest or constant speed.
they are not equivalet I know, I am not smarter than Issac Newton , but why I am wrong?
The first law defines inertial reference frames. Inertial reference frames are by definition reference frames in which the first law is valid.
After we have the definition of the inertial frames, we can formulate the second law: In all inertial reference frames F=ma.
The two laws can be of course formulated together: If a reference frame has the property that F=0 if and only if a=0, then in this reference frame F=ma.
So, there isn't redundancy.

thank you mma, so we have a difinition (or limitation) and two laws
its strange why many mechanics textbooks that I read doesn't refere to this point! maybe I have to read the principia because this formalism looks more historical than fundemental.

Vereinsamt said:
its strange why many mechanics textbooks that I read doesn't refere to this point! maybe I have to read the principia because this formalism looks more historical than fundemental.
I don't know, what textbooks do you mean. But I think that it isn't exceptional of interpreting the first law in this way. For example, Wikipedia writes:
Newton's first law appeared to be in the past just a special case of the second law, and it was thought Newton stated the first law separately simply in order to throw down the gauntlet to the Aristotelians. However, modern physicists think that the First Law defines the reference frames in which the other two laws are valid. These reference frames are called inertial reference frames or Galilean reference frames, and are moving at constant velocity, that is to say, without acceleration.
(see http://en.wikipedia.org/wiki/Newton%27s_first_law)