# What is the difference between Newton's first & third law?

Newton first law states that object stays in fixed state, unless external force is applied.

Newton third law states that: if there is action then there will be opposite & equal reaction.

So if we apply external force on object nothing but a action, so object moved is nothing but a reaction. So newton first & third law are same?

• – glS Dec 26 '14 at 9:45
• Also related is this answer, regarding the action-reaction matter. Could you also please clarify the statement (V2) "So if we apply external force on object nothing but a action"? As it stands it does not make much sense – glS Dec 26 '14 at 10:08
• @user36790 : it's not a sin when somebody doesn't know. To the contrary, when someone doesn't know, he/she asks, and that's very well. – Sofia Dec 26 '14 at 20:07
• @user36790: we have a rule, "be nice". It's the rule of Phys.SE. But, beyond the rule, we have to help. There where teachers, books, etc., leave things unclear, it's our place to help. This is why people apply to this forum. – Sofia Dec 27 '14 at 7:55

Newton's first law says that unless an object is applied a force it will continue its motion with the same velocity (or linear momentum). This law expresses the homogeneity of the Euclidian space: nothing changes from one place in the space to another.

Newton's third law says that if a body A acts on a body B by a force $\vec F$, then the body B acts also on the body A by a force $-\vec F$. What you say "So if we apply external force on object (is) nothing but a action, so object moved is nothing but a reaction", is not correct because the force you name "action" acts on you object - let's call it B - and reaction is a force with which B acts back on the object - let's call it A - that applied the force on B.

Though there is some truth in your idea, in the sense that from the 3rd law one can conclude the following: taking the two objects, A and B as a system, the forces applied by the parts of the system (A and B in our case) on one another, won't change the state of movement of the system as a whole.

• When you say "This law expresses the homogeneity of the Euclidian space: nothing changes from one place in the space to another", it might be helpful to explain that you are talking about Noether's theorem, which relates a number of physical symmetries to conservation laws (in this case, the fact that the laws of physics are translation-invariant, not varying from one point in space to another, can be used to derive the fact that momentum is conserved). – Hypnosifl Dec 26 '14 at 18:14
• @Hypnosifl: Why won't you post an additional answer and explain these interesting things? It would be a good idea. Just, please explain in a concise form, remember that long explanations may be tiresome. – Sofia Dec 26 '14 at 19:38

There is a sense in which the first and third laws are the same, because the are both just saying that momentum is conserved. The first law tells us that the momentum of an isolated object remains constant, and the third law tells us that the net change of momentum in any interaction between two bodies is zero i.e. momentum is conserved.

So both laws can be deduced from the statement that momentum is conserved. These days we would derive this from symmetry principles.

• @Sofia: it's not my intent to plagiarise your answer, or any other answers. However I strive always to identify the key feature of any problem then state that feature as clearly as possible. In this case I felt that although your answer is fine, I could improve on the clarity of it. Whether I've succeeded or not is for others to judge. – John Rennie Dec 26 '14 at 16:05
• I instantly apologize, and I insist on my apology. But, to put it in short, action and reaction act on different objects. Are you sometimes in the chat room? As you are a moderator, I would like to chat a bit with you about answers in general, all sort of forms of answer. – Sofia Dec 26 '14 at 20:03
• @Sofia: I'm not a moderator I'm afraid. I've just been around so long that everyone thinks I'm part of the furniture :-) – John Rennie Dec 27 '14 at 6:45
• But you are one who votes when a question is to be put on hold, or closed, or reopen, such things. Well, still, there are things that I would like to have a chat with you, about answers that I see sometimes. So, are you sometimes in the chat room? – Sofia Dec 27 '14 at 7:50
• @Sofia: I don't hang around in the chat room, but I'm normally on the site around 09:00 to 10:00 GMT and I'm happy to chat if you're around as well. – John Rennie Dec 28 '14 at 6:10

Newton third law states that: if there is action then there will be opposite & equal reaction.

What you are missing is that the action and reaction forces apply to two different objects. Newton's third law says that if object A exerts a force on object B, then object B must necessarily exert an equal but opposite force on object A.

Just because two forces are equal but opposite does not mean that these forces are third law interaction pairs. For example, consider a book resting on a table. Gravity exerts a downward force on the book and the table exerts an equal but opposite upward force on the book. These are not third law forces. An easy test of whether two forces are third law pairs is to determine whether the two forces act on different bodies. In this example, both forces act on the book, and thus these two forces are not third law action-reaction forces. In this example, the third law reaction to the gravitational force exerted by the Earth on the book is a gravitational force exerted by the book on the Earth. The reaction to the upward normal force exerted by the table on the book is a downward normal force exerted by the book on the table.

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