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

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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.

Andrew D'ArcyPost authori like the guy standing on the plane 🙂

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

likeprestigePost authorThese 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!!!

Michael

metalking0206Post authornewton and sal rules!!! m/

ShazPost authori 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 🙁

ohh well i know i smashed the exam 😀 😀

great vid btw 🙂 can do some on transformation of matrix? My F.maths exam is cuming up soon nd i dont get 1bit of it lol

2KPost 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 LalaPost authorWill you ever do a calculus-based physics playlist?

F = dp/dt

Rez APost authorwill u do a quantum mechanix tutorial?

sammelief1Post authorthank you

DuckRabbitPost 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.

DuckRabbitPost 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 AlanPost authordaayuum no dislikes

onlyTutorPost author1:30-1:40 Can I hear a little hate on Einstein there?^^

rhymes116Post authordo engineering physics !!! 🙂

MrFriedTacoPost 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.

MrFriedTacoPost author@learning112233

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.

umraughPost authorI 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…..

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

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

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

Cameron KiesserPost authori saw this in my science class today. HI Mr. Cox.

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

AniXiaNPost authorWill Sal ever do a playlist for Physics C? XD

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

FrostPost authorno

Cameron BeltPost authorthrough experimenting

FrostPost authormass is not proportional to acceleration F=lambda m a not ma

Alvin TostigPost authorWhy can't these intellectuals use sensible language that people can understand?!

Aditya KudalePost authori guess i will leave school and join khan cademy LOL

Steven Alexander SmithPost authorDon't forget Nicolaus Copernicus, Johannes Kepler and Galileo Galilei!

German-AmericanPost authorShnee I learned it in second grade, tight before multivariate calculus. What about you?

samus1225Post authorf=ma. fullmetal alchemist

LanceTheWingmanPost authorGay

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

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

Sourabh SharmaPost authorok!! 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 OliPost authorWe neVer gEt Scientist Like Isaac Newton

If…

Coconut Had Fallen On His Head Rather Than Apple..LoL….!!

Ernest SooPost authorExcellent

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

FrostPost authorits no accurate all I am saying

Azael BarreraPost authorToo 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. Newton´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 BarreraPost authorNewton'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 BarreraPost authorKhan 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.

silverPost author8n

silverPost authorits 8N

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

SinhaleseDravadiaPost authorThanks Khan

Aishwarya BhattacharyaPost authorHey…makes thngs easier 😀 thnx guys…awwsum

shylildudePost authoryou sound like eric bogosian

Mr Pregnant - Atelston Fitzgerald Holder 1stPost authorI 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.

laylakisPost authorcan anyone explain to me why he said that 10 N = 10 kg.m / s^2 ?????

MariePost authorHi!

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

Business and Technology - A Pakistani PerspectivePost 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 DaryPost author4:14 "ass" hit it on repeat a few times its funny 😛

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

AerosciencePost author"Before Einstein showed up"

prateek gurjarPost authorkeep hitting number "5" for a nice dubstep noise

Zach WarnerPost authorAll of this is so wrong…

Akshay GargPost authoryour videos helped me a lot Thankyou

Rabab wasiPost authorIs unbalanced force , net force and external force the same as resultant force?

andre santosPost authoram 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 jeonPost authorhe uses such colorful pens!

btw, what program does he use?

Yanz LicPost authornice

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

YiiraPost authorThank you I passed physics because of you

Corra MPost authorthis video just saved my grade in science class, thank you!

Ali AlaidarousPost authori hate physics 🙁

Varun KhorasiaPost author😎

HagenPost authorCould 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 alsaeedPost authorbut why f=ma there is any proof of it

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

geeta budhijaPost authorit is very bad explanation

Robinson CairoPost authorAwesome ….. just fantastic UR channel is a blessing

ArulmozhivarmanPost authorThank you Sal. Owe u a lot

Richardezer ScroogePost authorI don't understand. How does 10 newtons equal 10 kg? That's impossible.

sadie smithPost authorokay then ill just find a calculator of some sort its fine

Yan AmorimPost authorWhy the second is squared

Competine - LeaPost authorYou confused me a lot the first 40 sec……

Mohamed ShariffPost author😕

Vortex ZPost authorwhy did you do this newten ):::

Muzaffar KhanPost authorsir 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 ChenPost authoryou talked about air resistance as an example other than friction, however air resistance, or drag, is a type of friction force

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

K4MYBROPost authorhit 3 constantly for somehing kul 😛

Faqeer MuhammadPost authorplease make a video on law of conservation of momentum

Daniel TruongPost authorIt is not a problem for me to do any Khan academy problems

yasmiiin !Post authorSo what is newtons 2nd law of motion??

IndifferentPost authorThank youuuu

AKHILESH KUMARPost authorThanks

Jinkstack SPost authorVery helpful. Thank you

Srinuvasulu MPost authorThey didn't use proper English

aldrin saraybaPost authorWhat if the mass is missing?

ryeven brix espiquePost authornow this can help me in exams

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

kratosPost authorGreat vid keep up the good work

ghostahmad2gPost authorHey I will subscribe to any one who’s going to subscribe for me

Nashi Allen_WestPost authorThank you

XXXSuperman81841XXXPost authori do not get it

Lunatic LogicPost authorok but how can u prove that f=ma