Newton’s second law of motion | Forces and Newton’s laws of motion | Physics | Khan Academy

Newton’s second law of motion | Forces and Newton’s laws of motion | Physics | Khan Academy

Articles, Blog , , 99 Comments

Newton’s First Law tells
us that an object at rest will stay at rest, and object
with a constant velocity will keep having that
constant velocity unless it’s affected by
some type of net force. Or you actually could say an
object with constant velocity will stay having a
constant velocity unless it’s affected
by net force. Because really, this
takes into consideration the situation where
an object is at rest. You could just have
a situation where the constant velocity is zero. So Newton’s First
Law, you’re going to have your constant velocity. It could be zero. It’s going to stay being
that constant velocity unless it’s affected,
unless there’s some net force that acts on it. So that leads to the
natural question, how does a net force affect
the constant velocity? Or how does it affect of
the state of an object? And that’s what Newton’s
Second Law gives us. So Newton’s Second
Law of Motion. And this one is maybe
the most famous. They’re all kind of
famous, actually. I won’t pick favorites here. But this one gives us
the famous formula force is equal to mass
times acceleration. And acceleration is
a vector quantity, and force is a vector quantity. And what it tells us–
because we’re saying, OK, if you apply
a force it might change that constant velocity. But how does it change
that constant velocity? Well, let’s say I have
a brick right here, and it is floating in space. And it’s pretty nice for us
that the laws of the universe– or at least in the classical
sense, before Einstein showed up– the laws of
the universe actually dealt with pretty simple mathematics. What it tells us is if
you apply a net force, let’s say, on this
side of the object– and we talk about net force,
because if you apply two forces that cancel out and that
have zero net force, then the object won’t change
its constant velocity. But if you have a
net force applied to one side of this
object, then you’re going to have a net acceleration
going in the same direction. So you’re going to have
a net acceleration going in that same direction. And what Newton’s
Second Law of Motion tells us is that acceleration
is proportional to the force applied, or the force
applied is proportional to that acceleration. And the constant
of proportionality, or to figure out what you have
to multiply the acceleration by to get the force, or what you
have to divide the force by to get the acceleration,
is called mass. That is an object’s mass. And I’ll make a
whole video on this. You should not confuse
mass with weight. And I’ll make a whole
video on the difference between mass and weight. Mass is a measure of
how much stuff there is. Now, that we’ll
see in the future. There are other things
that we don’t normally consider stuff that
does start to have mass. But for our classical, or at
least a first year physics course, you could
really just imagine how much stuff there is. Weight, as we’ll see
in a future video, is how much that stuff
is being pulled down by the force of gravity. So weight is a force. Mass is telling you how
much stuff there is. And this is really neat that
this formula is so simple, because maybe we could have
lived in a universe where force is equal to mass squared
times acceleration times the square root of acceleration,
which would’ve made all of our math much
more complicated. But it’s nice. It’s just this constant
of proportionality right over here. It’s just this nice
simple expression. And just to get our feet wet
a little bit with computations involving force, mass,
and acceleration, let’s say that I have a force. And the unit of force
is appropriately called the newton. So let’s say I have a
force of 10 newtons. And just to be clear, a
newton is the same thing as 10 kilogram meters
per second squared. And that’s good that a newton
is the same thing as kilogram meters per second squared,
because that’s exactly what you get on this side of the formula. So let’s say I have a
force of 10 newtons, and it is acting on a mass. Let’s say that the
mass is 2 kilograms. And I want to know
the acceleration. And once again, in this video,
these are vector quantities. If I have a positive
value here, we’re going to make the assumption
that it’s going to the right. If I had a negative value, then
it would be going to the left. So implicitly I’m
giving you not only the magnitude of the
force, but I’m also giving you the direction. I’m saying it is to the
right, because it is positive. So what would be acceleration? Well we just use f equals ma. You have, on the
left hand side, 10. I could write 10
newtons here, or I could write 10 kilogram
meters per second squared. And that is going to be
equal to the mass, which is 2 kilograms times
the acceleration. And then to solve
for the acceleration, you just divide both
sides by 2 kilograms. So let’s divide the
left by 2 kilograms. Let me do it this way. Let’s divide the
right by 2 kilograms. That cancels out. The 10 and the 2, 10
divided by 2 is 5. And then you have kilograms
canceling with kilograms. Your left hand side, you get
5 meters per second squared. And then that’s equal
to your acceleration. Now just for fun, what happens
if I double that force? Well then I have 20 newtons. Well, I’ll actually work it out. Then I have 20 kilogram
meters per second squared is equal to– I’ll
have to color code– 2 kilograms times
the acceleration. Divide both sides by 2
kilograms, and what do we get? Cancels out. 20 divided by 2 is 10. Kilograms cancel kilograms. And so we have the
acceleration, in this situation, is equal to 10 meters
per second squared is equal to the acceleration. So when we doubled the force–
we went from 10 newtons to 20 newtons– the
acceleration doubled. We went from 5 meters
per second squared to 10 meters per second squared. So we see that they are
directly proportional, and the mass is that how
proportional they are. And so you could imagine what
happens if we double the mass. If we double the mass in this
situation with 20 newtons, then we won’t be dividing
by 2 kilograms anymore. We’ll be dividing
by 4 kilograms. And so then we’ll have 20
divided by 4, which would be 5 and would be meters
per second squared. So if you make the mass
larger, if you double it, then your acceleration
would be half as much. So the larger the mass
you have, the more force you need to accelerate it. Or for a given force, the less
that it will accelerate it, the harder it is to change
its constant velocity.

99 thoughts on “Newton’s second law of motion | Forces and Newton’s laws of motion | Physics | Khan Academy

  • Andrew D'Arcy Post author

    i like the guy standing on the plane πŸ™‚

  • Jold Post author

    I never really understood why the first and second laws are separate. F=ma implies the first law – if F=0, then a=0.

  • likeprestige Post author

    These videos on physics are great Sal, I've just commenced -introduction to physics- & so far your videos are really helping me out. I've also started coaching my 7 year old niece (lives in a different state) in math via your main website, khan academy & things are going great there also, thanks to you she is making so much progress!

    From Sydney, Australia, I say thank you!!!


  • metalking0206 Post author

    newton and sal rules!!! m/

  • Shaz Post author

    i wish u had done all of these physics vids about 5days ago, u r literally going through all of ma syllabus…..could have helped so much with my AS physics exam πŸ™

    ohh well i know i smashed the exam πŸ˜€ πŸ˜€
    great vid btw πŸ™‚ can do some on transformation of matrix? My F.maths exam is cuming up soon nd i dont get 1bit of it lol

  • 2K Post author

    @elfmotat The second law expands the first one. The first law is separate so that the concept is clearly spelled out because not everyone will deduce the first law from the second. And the second law expands the first by telling us how to figure out how much force is being or was applied to the object.

  • Hot Pepper Lala Post author

    Will you ever do a calculus-based physics playlist?

    F = dp/dt

  • Rez A Post author

    will u do a quantum mechanix tutorial?

  • sammelief1 Post author

    thank you

  • DuckRabbit Post author

    @learning112233 the (negative) acceleration of the car when it hits the wall would be equal to the change in speed of the car when it hit the wall(from 50mph to 0mph assuming the wall stopped it) divided by the period of time in which the car decreased its velocity (it isn't zero, it's just a short period of time). Now that you have the acceleration, you multiply it times the mass of the car to get the force applied on the wall.

  • DuckRabbit Post author

    @learning112233 Actually, if we throw a ball in space the only moment in which we applied force to it is when we threw it. Only in that moment it accelerates, in every other moment before that its velocity is constant and equal to the velocity it had when we threw it.

  • Breezy Alan Post author

    daayuum no dislikes

  • onlyTutor Post author

    1:30-1:40 Can I hear a little hate on Einstein there?^^

  • rhymes116 Post author

    do engineering physics !!! πŸ™‚

  • MrFriedTaco Post author

    @learning112233 Yes, but Newton's laws do not include the inaccuracies that show up in more advanced + modern based physics. Newton at the time did not know the maximum speed.

  • MrFriedTaco Post author


    Friction acts on and slows down the car. The balancing of the force of the car and the friction on the ground result in a net force of zero. Therefore, in fact the force of the car is zero.

    The formula stated is not technically correct. it is Fnet = ma

    This is why confusion arose.

  • umraugh Post author

    I mean i like physics but seriously didnt isaac newton hooke and all the others have a life. I mean sitting down and watching random stuff…..

  • TheSimian Post author

    Why do objects of differing mass fall at the same rate (assuming no resistance)? Is there a video that explains this phenomenon?

  • sci gee Post author

    @Freakingeediot thank you for the reply …. i also had the same question

  • Jason Tree Post author

    @gooseCha lol this is what you arre studying in university, damn you are far behind.

  • Cameron Kiesser Post author

    i saw this in my science class today. HI Mr. Cox.

  • Kiwimaru Post author

    How does one figure out how much force is needed to break something? Like how much force to demolish a brick wall?

  • AniXiaN Post author

    Will Sal ever do a playlist for Physics C? XD

  • Frost Post author

    F=ma is a lie, its F=Ξ³^3ma where Ξ³=1/sqrt(1-v^2/c^2)

  • Frost Post author


  • Cameron Belt Post author

    through experimenting

  • Frost Post author

    mass is not proportional to acceleration F=lambda m a not ma

  • Alvin Tostig Post author

    Why can't these intellectuals use sensible language that people can understand?!

  • Aditya Kudale Post author

    i guess i will leave school and join khan cademy LOL

  • Steven Alexander Smith Post author

    Don't forget Nicolaus Copernicus, Johannes Kepler and Galileo Galilei!

  • German-American Post author

    Shnee I learned it in second grade, tight before multivariate calculus. What about you?

  • samus1225 Post author

    f=ma. fullmetal alchemist

  • LanceTheWingman Post author


  • Adam Thornton Post author

    I always thought a=f/m was a more intuitive way of stating this law.

  • Joey Smith Post author

    Newtons Second Law is to advanced for children. Maybe you should start with proper use of periods before anything.

  • Sourabh Sharma Post author

    ok!! so u can calculate the amount of force applied on an object by multipling its mass with the acceleration gained by the obj…
    my ques. is .. can't i calculate the amount of force exerted by any object of mass 'x' and that is travelling at certain speed 'y' ? like for example how much force would a car exert if it collides with a wall or how much force would a kick exert given its mass and speed/acceleration ??

  • Sumit Oli Post author

    We neVer gEt Scientist Like Isaac Newton
    Coconut Had Fallen On His Head Rather Than Apple..LoL….!!

  • Ernest Soo Post author


  • Andrew Burns Post author

    thank you so much sir this is helping me a lot thanks again keep the great work up

  • Frost Post author

    its no accurate all I am saying

  • Azael Barrera Post author

    Too bad Khan Academy starts explaining Newton's First Law of Motion using Newton's own text from Principia, but does not do the same with Second Law and fall in the same huge mistake physics teachers have gone through for decades. NewtonΒ΄s Second Law, if KA is consistent says other wise, it is not F = ma, it describes the change in quantity of motion -defined in the Definitions in Principia as what we now know as momentum- or mass times velocity, as a result of the application of a force.

  • Azael Barrera Post author

    Newton's second law clearly says that the quantity of motion (m x v) will change as a result of the application of a impressed force and will do so in the same direction, straight line, as the impressed force direction. Here Newton implies direction, that is introduces the concept of vector as applied to the forced and the quantity of motion. That is the real Newton's Second law, it relates force with change of quantity of motion (m x v).

  • Azael Barrera Post author

    Khan Academy does a good job for online education and supplementing class instruction, but please, if the original First Law by Newton is used from Principia, use the other two laws also from Principia. BE consistent.

  • silver Post author


  • silver Post author

    its 8N

  • Doodelay Explains Post author

    If everything in free fall floats and everything in space floats than the universe itself must therefore be falling?

  • SinhaleseDravadia Post author

    Thanks Khan

  • Aishwarya Bhattacharya Post author

    Hey…makes thngs easier πŸ˜€ thnx guys…awwsum

  • shylildude Post author

    you sound like eric bogosian

  • Mr Pregnant - Atelston Fitzgerald Holder 1st Post author

    I see a strong correlation between Hegelian's Dialectics; Thesis-Antithesis-Synthesis, and Newtons Laws of Motion. Antithesis is the contrast or opposition of an idea or concept, and synthesis is the unified whole of mutually exclusive elements, or the reconciliation of contradictory ideas where a new idea is formed, and this concept has been perfectly demonstrated within the medical context. Our perception of the world is constructed around polar opposites, a notion demonstrated in Issac Newton's Three Laws of Motion, a law in nature that laid the foundation for classical mechanics.

    Primarily the "Third Law" which states; every force or action is contingent on an equal reactive force. Meaning if you push a cup on a table, it's motion and velocity should be perpetual, but what hinders or constricts is movement is an external force; like the friction on the table applied contrastingly to the cup in motion, hence it stops. Or the "First Law" which states; an object in uniform motion stays in motion unless acted upon by any given force.

  • laylakis Post author

    can anyoneΒ explain to me why he said that 10 N = 10 kg.m / s^2 Β ?????Β 

  • Marie Post author

    I don't really understand what a net force is?

  • Business and Technology - A Pakistani Perspective Post author

    @timbar4 You are talking about energy. How much energy was spent pushing or applying force to an objects is determined by obtaining the vector product ( a type of multiplication ) of force and displacement. There is no such thing as a total force. Force is determined for a specified instant in time. Like what is the force 'now'? You cannot take a total of force. That would be wrong. There is net force, though. Just make do with that.

  • Zonon Dary Post author

    4:14 "ass" hit it on repeat a few times its funny πŸ˜›

  • Ahsen Kamal Post author

    plz tell that which object's MASS is more – 1kg iron or 1kg cotton?

  • Aeroscience Post author

    "Before Einstein showed up"

  • prateek gurjar Post author

    keep hitting number "5" for a nice dubstep noise

  • Zach Warner Post author

    All of this is so wrong…

  • Akshay Garg Post author

    your videos helped me a lot Thankyou

  • Rabab wasi Post author

    Is unbalanced force , net force and external force the same as resultant force?

  • andre santos Post author

    am i the only one thats annoyed everytime he writes a word? like everytime he writes something he need to say it like a hundred times

  • leein jeon Post author

    he uses such colorful pens!
    btw, what program does he use?

  • Yanz Lic Post author


  • Roberto Sanchez Post author

    (I want to use the acceleration)^3 before getting to your point…

  • Yiira Post author

    Thank you I passed physics because of you

  • Corra M Post author

    this video just saved my grade in science class, thank you!

  • Ali Alaidarous Post author

    i hate physics πŸ™

  • Varun Khorasia Post author


  • Hagen Post author

    Could you simply divide the amount of force [10 in this case] by the mass [2 in this case]? Is this situational or is it a strategy that would work?

  • mousa alsaeed Post author

    but why f=ma there is any proof of it

  • Keshav Rawat Post author

    if i push something (applying force) without accelerating it does that mean I am not applying any force?

  • geeta budhija Post author

    it is very bad explanation

  • Robinson Cairo Post author

    Awesome ….. just fantastic UR channel is a blessing

  • Arulmozhivarman Post author

    Thank you Sal. Owe u a lot

  • Richardezer Scrooge Post author

    I don't understand. How does 10 newtons equal 10 kg? That's impossible.

  • sadie smith Post author

    okay then ill just find a calculator of some sort its fine

  • Yan Amorim Post author

    Why the second is squared

  • Competine - Lea Post author

    You confused me a lot the first 40 sec……

  • Mohamed Shariff Post author


  • Vortex Z Post author

    why did you do this newten ):::

  • Muzaffar Khan Post author

    sir acceleration 'a' is applied opposite direction to the applied force bcz ( F=ma) F+(-ma)=0 in equilibrium condition bt show it in same direction i think its wrong

  • Qianhua Chen Post author

    you talked about air resistance as an example other than friction, however air resistance, or drag, is a type of friction force

  • Abdullah A Alnaser Post author

    Khan Academy you just saved me from midterm exams, thanks so much. I hope you reupload more about physics again 2018!

  • K4MYBRO Post author

    hit 3 constantly for somehing kul πŸ˜›

  • Faqeer Muhammad Post author

    please make a video on law of conservation of momentum

  • Daniel Truong Post author

    It is not a problem for me to do any Khan academy problems

  • yasmiiin ! Post author

    So what is newtons 2nd law of motion??

  • Indifferent Post author

    Thank youuuu

  • AKHILESH KUMAR Post author


  • Jinkstack S Post author

    Very helpful. Thank you

  • Srinuvasulu M Post author

    They didn't use proper English

  • aldrin sarayba Post author

    What if the mass is missing?

  • ryeven brix espique Post author

    now this can help me in exams

  • Mr QoSz Post author

    Why does this look simple but when I go into the exam it's way harder like come on life is really tuff

  • kratos Post author

    Great vid keep up the good work

  • ghostahmad2g Post author

    Hey I will subscribe to any one who’s going to subscribe for me

  • Nashi Allen_West Post author

    Thank you

  • XXXSuperman81841XXX Post author

    i do not get it

  • Lunatic Logic Post author

    ok but how can u prove that f=ma

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