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Forces and Newton's laws of motions

Henry Tan's picture

Newton's laws of motion

An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

For every action, there is an equal and opposite reaction.

back to MACE-11010  Engineering Mechanics


Henry Tan's picture

Newton’s first law is only a special case of the second law: the acceleration is zero when the applied force is zero.

The Three Laws can therefore been reduced to Two Laws.

Why the first law is listed as one of the Three Laws, and the 1st one? There must be a reason, what is that?

Ying Li's picture

I think it is the sequence of the thinking. Firstly, Newton noted that the static object will be static or the motion object will keep motion if no force applied on it. However, it is only ideal situation. Then he takes the real factors in to the consideration. And he fond that the change of the momentum is the reason for the acceleration existing. Therefore, the Firs law is the ideal situation and the second law is the real situation.

Temesgen Markos's picture

The original version of Newton's second law states that the rate of change of "quantity of motion" is proportional to the force applied. That quantity of motion Newton referred to was momentum.

Newton's second law has been perverted later and stated F=m*a which agrees with Newton's version only when the mass remains constant. Probably we use this version since it is what usually happens in every day life.

I don't think the F = d(m*v)/dt reduces to the first law in the case of zero acceleration.

Btw F=m*a is one of the things I learned at school and had to unlearn later.


The word perversion is too strong.

The difference between F = dp/dt and F = ma is not so much relevant in any classical context, including those wherein mass varies classically. The difference between the two definitions matters only in the relativistic contexts.

Now, if one is at all going to go back to Newton's original ideas, one might as well stay consistent and thereby include his original ideas of the absolute space and the absolute time as the notions given prior to the discourse, and on such a basis, describe the very idea of a reference frame as a perversion. Now, how does *that* sound?

[BTW, I don't at all mind using strong words, but just think that the present matter doesn't need it, that's all.]

Teng zhang's picture

I think the first and secon Newton's laws of motion is to find a function to describe the relationship between force and acceleration, in the form of F=F(a). As Markos said, if the mass remains consant, the first law tells us F(0)=0 , which should be satisfied for the function we find first. I think that's mabe the reson that the first law is listed as the 1st one.

Henry Tan's picture

Newton’s second law actually defines what the FORCE is.
Then the second law is not a law at all, but actually just a definition for FORCE.

Correct me if I am wrong.

0. It's impossible to be concise on a set of laws which are some 350 years old and lie at the base of all of engineering and most of physics. Tomes have been written on those three concise statements alone. But attempting to give a concise comment, here is my informal take on the matter (in the off-the-cuff way, without thinking too much about it before writing):

Each law (of Newton's) is like the apex of a long thought process, each being intimately interconnected with the other two.

1. The first law introduces the (physically) universal attribute of inertia. It gives the *limiting* conditions under which the existence of this attribute can be most easily grasped.

2. The second law introduces and defines the quantity called force. A definition can be a law. (Incidentally, this is one way it can be justified that force has be an axiomatic concept in mechanics.)

3. The third law introduces, in a sense, that idea which is best described as a conservation principle.

If one lets go of all physical and geometric reasoning preceding the laws, and admits into his analysis only a mathematically expressible abstraction of the facts denoted by the three laws, then it's obvious that the second law would be quite enough, because that is all the mathematics there really is to Newton's laws--the *mathematics* of the other two laws being simply corollaries. But this does not, therefore, mean that the physical notions involved in the other two laws are also deductively given by the second law. For instance, inertia is an idea whose meaning can be grasped without having defined force--even if the two are intimately related. (Indeed, Galileo had already grasped the idea of inertia very clearly, but, apparently, not of force.)

Mahendra Gattu's picture

I was recently asked to tell the newtons second law of motion and I promptly replied F=ma. Later I was asked about the validity for a rocket. Then I gave a more general definition of F=dp/dt. I thought why I replied in that manner. I remember the first time I learnt the Newtons Laws of motion, F is directly proportional to ma,=>F=kma,For F=1,m=1,a=1, k=1. => F=ma and 1N=1kg m/s2

Ajit ji are you driving at the idea that motion(kinematics) is more fundamental than force. I have some questions in mind regarding which is more fundamental strain or stress. Consider a metal rod which is heated in between two rigid supports and constrained laterally. It tries to expand.There is no observable deformation. However, there is an intutive feeling of some kind of push acting on the rigid  supports and  some kind of compression on the metal rod.


Also there is another line of thought. Can Energy be treated as the most fundamental quantity, say for a simple body of mass m moving at velocity v, KE= p2 /2m , d(KE)/dt=2pdp/dt=0. (p=mv). I had this line of thought when I was introduced to the concepts of strain energy and complementary strain energy during basic structural analysis classes.I thought about it for sometime and didnt pursue it further.

1. I am not a "purist" either for or against relativity or Newton's theory. Funny, but it invariably so happens (to me) that in the context of UG courses on mechanics in engineering, I, by default, think of F = ma. But not so when I am thinking of the UG courses in physics. There, I do think of things like F = dp/dt, and even other ideas like the Hamiltonian formulation, etc.--the ideas which I don't think of in engineering contexts. Overall, I tend to be comfortable any of the ways force is defined: I just make an educated guess about the context the speaker assumes, that's all. In this thread, the context is: Newton's laws, in UG engineering course.

2. I am not at all discussing whether motion is more fundamental than force. In fact, I have avoided such a discussion even in the thread on why strain is more fundamental than stress, in reply to Grant Henson's comment, here. The reason is that one ought to be careful not to trample on the cognitive coherence of a particular thread. (It's funny that people take so much extra care, even of the useless sort, not to hurt others' "sensitivities", but apparently none advocates doing so for cognitive coherence or conceptual cohesiveness--i.e. for integrity of knowledge.) So, of course, if you want it discussed (fundamentality of motion, force, energy, etc.), then I think you should go ahead and create a separate thread! I will feel freer (and so, happier) to respond there.

3. About stress or strain. See the answer on the appropriate thread, here.

4. Finally, I think, a gentle nudge about minimization of thread-jumping would be in order. And, while at it, may I, perhaps, remind you about visiting this topic as well?

Henry Tan's picture

Actually, the 3rd law can also be deduced from the 2nd law. Therefore, Newton’s THREE laws reduce to only ONE law (so called 2nd law), which is only a definition.

Gopinath Venkatesan's picture

I think, because Newton indicated the direction of net force in a definite sense, it could also be called as a law. The direction of force (reaction in 3rd law) is specified in all the three laws.

I humbly request a small addition to the 3rd law. Action and reaction are equal and opposite, true. However, they act on two different bodies. Wasn't this a part of Newton's Third Law as well? Well, that's what they taught me at high school.

 3rd Law - For every action, there is an equal and opposite reaction, and they act on different bodies.

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