# Newton’s Second Law of Motion

Welcome back. We’re now ready for Newton’s
second law. And Newton’s second law can
simply be stated– and you’ve probably seen this before as
force is equal to mass times acceleration. This is probably, if not the
most famous formula in all of time or all of physics,
it’s up there. It’s probably up there with
E equals mc squared. But that one’s a little
bit more complicated. So what does this tell us? This tells us that the force,
the net force upon an object, is equal to the object’s mass
times its acceleration. So let’s stay in the metric
system because most of what you’ll do in physic class is in
the metric system, and that tends to be because the metric
system makes more sense. So let’s say that I have
a 1 kilogram object. So its mass is 1 kilogram. And it’s being pulled down
at– let’s say its acceleration. It’s being accelerated downward
at 9.8 meters per second squared. These kind of units should be
familiar with you from all the projectile motion problems. So the force applied on that
object in order to get this type of acceleration would be–
you just multiply mass times acceleration. The force would have had to be
9.8 kilogram times the meter. kilogram. times meter over
second square. That’s the force applied
on the object. And you’re saying, sal,
this is very messy. I don’t like writing kilogram
meters per second squared. And you are in luck because
there is a unit and that unit is the Newton. 1 Newton is equal to 1 kilogram meter per second squared. So if I’m pulling down on an
object at 9.8 Newtons, that’s just this, right? This is 1 Newton. If I’m pulling down at 9.8
Newtons on an object that is 1 kilogram, its acceleration is
going to be 9.8 meters per second squared down. And notice I said the word down,
but I didn’t write it anywhere in the formula. And I guess we can imply that
both force and acceleration have direction by writing
this in the formula. That force is a vector and
acceleration is a vector. And so we could have written
9.8 Newtons– I don’t know. You’ll never see this
convention. We could say Newtons down is
equal to 1 kilogram times 9.8 meters per second down. So what can we do with
this formula? Well we can solve problems.
So let’s say that I have an object. So my object weighs–
not weighs. The mass of my object. And I’ll differentiate between
weight and mass in a second. Let’s say the mass of some
object is– I don’t know– 50 kilograms. That’s how much a
normal person might weigh or a light person. Mass weighs 50 kilograms. And
let’s say we’re in an inertial frame of reference. We’re in deep space, so we don’t
have all these other– the force of wind and
the force of gravity acting on us, et cetera. My force, let’s say I apply
it to the right. So we know that force
is a vector. Let’s say I apply a force of–
I don’t know– 100 Newtons. And let’s say I apply
it to the right. So this is the object, 50
kilograms. And I’m applying a force to the right
of 100 Newtons. So what’s going to happen
to this object? Well, let’s use the formula. Force is equal to mass
times acceleration. The force is 100 Newtons. 100 Newtons is equal
to the mass. The mass is 50 kilograms.
50 kilograms times the acceleration. So we can divide both sides by
50 and you get 100 Newtons over 50 kilograms is equal
to the acceleration. And it’s 100 Newtons
to the right. I’ll use this little
arrow here. That’s not a traditional
convention, but that’s how we know it’s to the right. So it’s 100 divided by 50. So it’s 2. We get this weird units here,
Newtons per kilogram is equal to the acceleration
to the right. This is also going to be to
the right because the direction of the force is going
to be the same as the direction of the acceleration. So what is this, 2 Newtons
per kilogram? Well, if you remember– well you
could just guess that the unit of acceleration is meters
per second squared. But let’s show that this
simplifies to that. So we said earlier that– let
me just switch colors. That a Newton is kilogram meter
per second squared. And we’re taking this Newton
over this kilogram over kilogram, right? So that will cancel out with
that and you get meters per second squared. And you wouldn’t have to do this
on a test. Essentially, if you did everything right, you
would know that the unit acceleration is meters
per second squared. So you would have the
acceleration– I’m just switching the two sides–
is equal to 2 meters per second squared. And it’ll be to the right. So that’s useful. We just figured out based on how
hard I push something, how fast it’s going to accelerate
while I push it. And you could use the
same formula to figure out other things. Let’s say I know that an object
is accelerating– let’s say my acceleration is
3 meters per second squared to the right. Let’s say to the left, just
to switch things. And let’s say that I know the
force being applied on it is– I don’t know– 30 Newtons
to the left. And I want to figure
out the mass. Well you use the same thing. You say force, 30 Newtons to
the left is equal to mass times acceleration. Times 3 meters per second
squared to the left. Divide both sides by the 3
meters per second and you get 30 Newtons over 3 meters
per second squared is equal to the mass. 30 divided by 3 is 10. You can figure out that Newtons
is kilogram meters per second squared. So you’re just left with
10 kilograms is equal to the mass. It’s very important that if you
see a problem where the answer’s given in– I don’t
know– kilometers per second squared or you know, instead of
giving it in kilograms it’s giving it in grams or decagrams,
you should convert back to kilograms or meters just
so you make sure you’re using the right units. And that tends to be frankly,
I think, the hardest thing for people. And we’ll do all of that when
we tackle harder problems. I think now is a good time back
to actually differentiate between mass and weight. And you’ve probably thought the
two were interchangeable, but they’re not. Mass is how much of an
object there is. You can almost view it as how
much of the stuff there is or you can almost it view it–
how many atoms there are. But even atoms have mass. So just how much
stuff there is. And another way to view mass is,
how much does the object resist change? And that actually falls
out of F equals ma. Because if our mass is bigger,
it’s going to take a lot more force to make it accelerate
a certain amount. If the mass is smaller it’ll
take less force. So mass can be viewed as how
much stuff there is, of an object there is. Or you can view it as how hard
is it to change what that object is doing. If it’s stationary, how hard
is it to accelerate it? If it’s moving, how hard
is it to maybe stop it? Which would essentially
be decelerating. How hard is it to accelerate
an object? Weight is actually how much
is– what is the force of earth upon an object? So you’re weight would actually
change if you go from one planet to another because
the force of gravity changes. So your weight is 1/6 on the
moon as it is on earth because the pull of gravity is 1/6. But your mass doesn’t change. There’s still the same amount
of Sal on earth as there is on the moon. So your weight really– when you
ask someone in Europe and they say hey, you know, I weigh
50 kilograms. You should say, no, you don’t weigh 50
kilograms. You weigh whatever 50 times 9.8 is. That’s like 400 something–
you weigh 490 Newtons or something. This is mass. And it’s interesting because in
the English system, and all of us Americans, we use
the English system. When we say that we weigh 10
pounds, we’re actually using the correct terminology
because pounds are a unit of force. We’re saying, if I weigh– and
I do weigh about 150 pounds. That means the earth is this
pulling on me with 150 pounds of force. And actually, turns out that
my mass is measured in the unit called a slug, which
we might discuss later. Actually, we’ll do some problems
where we do it in the metric system and the
English system. And I’ll see you in the
next presentation.

## 100 thoughts on “Newton’s Second Law of Motion”

• ### Natawat Post author

Proved useful, thanks. ๐

• ### Cody Slab Post author

Igor watched this

Thank you!

• ### David Le Post author

THIS IS VERY HELPFUL THANK YOU

• ### sn81 Post author

what a great video. I am a physics student and i will say that you got everything right, and that this vid will be quite helpful to many. it doesnt get any more user friendly than that! let's not glorify the english system though by saying it is correct cuz it measures pounds on a scale. the english system is obselete. can we please move on??

• ### santagotgangbashed Post author

i left my science book at school.. got a test lesson 1 tomorrow…

saved my ass ๐ thanks mate

• ### Joseph Hamarich Post author

Even if I fail this test, you have been insightful

• ### Jason Newton Post author

my last name is newton ๐

• ### TheOnlyMohammed Post author

WHAT IS A VECTOR I HAVE SEARCHED THE NET AND I STILL CAN'T UNDERSTAND IT can u help explain

• ### Chris Bianchini Post author

he has a video about vectors… im not sure if it is important anymore but he does

• ### Nutterbutterz95 Post author

It's basically just a magnitude (like speed) in a direction (to the left).

Think of a tornado. A vector that represents a tornado could be something like 500 mph toward someone's house. Obviously a grim example, but I hope it explains.

• ### Nutterbutterz95 Post author

It's really just for the sake of reference. I, for one, should know whether or not a ball is going toward me, or toward the ground. Speed, the scalar, is really unspecific.

• ### Rory O'Connell Post author

The law he works out if F=MA.
Force = Mass multiplied by acceleration

Force is what is called a vector. A Vector is a unit of magnitude and direction. How fast something is moving and in which direction it is moving in.

As opposed to a vector, a Scalar only requires magnitude. If you just give an acceleration of 3 metres per second squared, that is a scalar.
However if you give 3 metres per second squared to the left, that is a vector.

• ### Rory O'Connell Post author

You can give more specific terms of direction. For example you could say 20 degrees North of West.

I hope that clears it up for you, however if you need anymore clarification I would be happy to offer an explanation.

• ### k1773ns Post author

๐ฎ thanks that really helped me with my homework !
—k

is there already a symbol or or equation showing the absence of all forces such as deep space? just a question.

• ### Vladimir Krylov Post author

This is soo much more sence then sitting in the class and listening to the teacher -.- Thanks mate!

• ### crystalidx Post author

@vlad7753 yeah i was having so much confusion! everyone in my class seem to be kk expect for me.

• ### Bonnie Lam Post author

Thank you so much for your explanation as I felt so confusing to the third law before that;)

ms^-2!!

• ### avantgardener3 Post author

Really clear. Thanks

• ### Hellsslave666 Post author

I always assumed that the metric system is better (im german hehehe, but with mass and weight the english system makes a lot more sense. I knew kg for weight is "wrong", but i didn't knew that lb is "correct"!
Thatks a lot!

• ### tbirdscience Post author

@MrGMauler

Objects most certainly do accelerate in space! Acceleration is defined as a change in velocity – and velocity is speed with direction. So…change the speed, you accelerate. Change the direction – you accelerate. So objects (such as the earth) that are orbiting an object (like the sun) are constantly accelerating because they are constantly changing direction.

• ### ChevailerNoir Post author

Yet another great video! Thank you!

Thank you!

NIce video

• ### Carl Benedict Monterroyo Post author

nice video thank you

• ### Cavin Dionel N. Batinga Post author

there! now i can report this thing… thankz

@danglang11
changing direction is acceleration because acceleration is defined as the change in velocity and velocity is the speed AND direction of an object ๐

• ### Gabe Gallegos Post author

why aren't there people like you in the classroom, instead of teachers that don't even explain things that well!!

• ### mike davinci Post author

thanx very much , and if i'm right then
F = ma
=m x v/t
F=momentum/time (momentum = mass x velocity)

• ### fcdog555 Post author

@floopsie666 wrong, F=dp/dt where p=m0v/sqrt(1-v^2/c^2)
Relativity ftw.

• ### Moonman2197 Post author

โข Its all wrong. Its called laws of Cuck Norris
1) Inertia: Objects will remain at rest or in a uniform motion in a straight line, unless acted upon by Chuck Norris.
2) Force, Mass, Acceleration: The acceleration of an object depends upon Chuck Norris and the magnitude of his force.
3) Action & Reaction: For every action there is an equal or opposite reaction (except with Chuck Norris, there is no such thing as an equal reaction, Chuck Norris is always one step ahead).

• ### keigerb19 Post author

thank you very much i need this for our homework

E=MCยฒ is false ๐

• ### SwagMcBaller Post author

yay! im learning! ๐

• ### Vladimir Krylov Post author

@tuesday2998 Well, it helped me, so that's what really matters ๐

• ### jaakbrel Post author

so when a boxer hits someone, it has to do with his mass and accaleration?

• ### tangredss Post author

how is newtons 2nd law of motion applied during a 100m sprint?

• ### Zach Lewis Post author

@tuesday2998 thats what his laws are about? math and physics.

• ### hexihaxi Post author

En bra video det hรคr Jan!
Hรคlsningar Klassen.. ๐

• ### 07spider123 Post author

THANK YOU SOOOOO MUCH

• ### Kortny Fitzsimmons Post author

What are three real life examples for this?

• ### MrAircraft999 Post author

thumbs up if you're learning this at school

• ### coolbrujah2 Post author

this is a great lesson, i have a question, and please bear in mind i know little of mathmatis, ans im arrempting to improve upon that, but, would a problem arise from the left side of the equation being done in metric, and the right in well, standard?

• ### kickodude Post author

Bro I love you. That is all. No homo of course.

• ### Iain Ilott Post author

In our physics class we use m.s(power of -2) and stead of m/s(power of2).. mathematically its the same thing, but its weird lol

• ### jbarah05 Post author

@zzzMegazzz Because one is your action force and the other is reaction force which are the same thing and expressing it with -2 is telling you which side your are working with

• ### Chirag Patel Post author

why do you teach online? you should be a professor!

• ### Ravyu Sivakumaran Post author

i know right, we do the same thing

• ### Ghost572 Post author

I assume if you threw a ball upwards it would gain potenial energy as it goes up and then gravity pulls the ball down which is 9.8 m/s2.

• ### Ghost572 Post author

Thanks for this vid man!

• ### George Washington Post author

home work done ๐

• ### melac12 Post author

Can someone please answer? If falling force is almost constant near earth, how come with the same farce object falling from higher distances hit the ground harder and with more impact, shouldnโt it be like if you want to hit something harder use more force. But in this case force is constant. I would appreciate if someone could help.

• ### Jonathan Portier Post author

much better than my teacher

• ### Eithan Maler Post author

So I ran upon a problem in physics where it said the objects mass and it's speed but not it's acceleration, how would I figure that put. If I use F=ma that would mean that 0N to keep it at that speed, and that doesn't quite make sense.

-high school physics student

• ### Adam Sharif Post author

@Ethan if the speed is constant then the acceleration is zero. If the speed changes between two time intervals use your kinematics to find a.

• ### itsmeTIBOR Post author

Honestly, If we were "learning" it, we wouldn't be here. No offence Khan Academy ๐

• ### Jamal Kettrell Post author

@khanacademy for the net force formula, you forgot to put the sigma sign behind the " f"

• ### slayerA0D Post author

What is mass?

• ### Ranish Chand Post author

the amount of matter in an object

• ### Christie W Post author

you are j.e.s.u.s

• ### Gaxa Glitz Post author

Just Exactly So Useful Seriously XD

• ### Michael Guo Post author

The first thing Sal should teach you is how to spell.

• ### forrstfire Post author

Sal should also teach you how to reply aswell

(you posted the comment 4 times)

• ### Jade Strider Post author

fuck college. this guy is awesome

• ### vin muru Post author

THANK YOU SO MUCH FOR YOUR COMMITMENT IT CHANGE LOT PEOPLE LIFES

Thank you!

• ### Ahmad Bintouq Post author

Thank u I understood in 9min what my teacher needed 2months and I didint understand

• ### asdf Post author

A force F causes an acceleration of 0.20 m s^-2 as he works on mass m1 and an acceleration of 0.30 m s^-2 as he works on a mass m2.
The acceleration in m s^-2, which causes a force 2F mass m1 and m2 together is
A: 0.24 m s^-2
B: 0.25 m s^-2
C: 0.48 m s^-2
D: 0.50 m s^-s

• ### abdellatef abdo Post author

Thank you Khan
respect from Morocco , Afrique , Earth .

• ### THE--FUZZZZ Post author

This guy would make such a great Jeff the Killer.

• ### MothBird Post author

Man this guy can explain a month of class work in 9mins so I can actualy pass my quiz

• ### Patrick Red Post author

then why would anyone watch the video?

• ### quantumechanick Post author

Let's replace college with Youtube. God knows I've learned more here than during lecture!

• ### Ken Smith Post author

common sense allows me to drag water on a wood pallet, with the force i drag it…the part you need to worry about is safty for others….math of such things are common sense….common sense and safty is actually not common though…and i dont care how smart anyone is…the common sense part is all that really matters, if everyone applied this we would have "communism" i like my role and care not the pay

I have an idiotic question but someone please refresh my mind

If you apply a constant force of 10N to a mass of 1kg, it will accelerate 10m/s^2 until the application of the force ceases, in which case the velocity of the mass will be whatever it was when the force stopped being applied.ย

Now to the question. If you bench press for instance (a small weight that you can do pretty much whatever you want to) you're applying a force to the weighted bar, right? However, the weight is not necessarily accelerating. Say you intentionally press the bar from your chest all the way up with a constant velocity (ofc t(0) won't be the same as after 2 seconds but anyway) of 0,2 m/s, what is the catch in that situation? A force must be applied constantly or the weight would drop on your chest, why isn't it accelerating?

• ### Daniel Dempster Post author

plz get a new mouse and write better, PLZPLZPLZ I <3 UR VIDS

• ### Mr Pregnant - Atelston Fitzgerald Holder 1st Post author

โNewtonโs Third Law of Motion,โ a law in physics that has stood the test of time. With exception ofcourse to the quantum world of improbability and ambiguity. Newtonโs first law of motion states that the uniform state of an object remains in motion unless disrupted by an external force. Second law states the relationship between object, mass and acceleration, (F is F = ma). The third law states; for every force in nature thereโs an equal opposite reaction. A propagating law in physics that you can analogically and metaphorically cross-platform into mutually exclusive fields; "figuratively," and would definitely stand the test of time.

Im 160,000

Im 160,000

• ### The Slice724 Post author

Is it net force or not?

• ### Byd Retros - PS3 Post author

thanks alot for your help ๐

• ### Bobby Millionaire Post author

Applying force or newtons to a mass – does this change the weight of the object? Thank you for the video.

• ### Mihika Sathe Post author

Wo!!!w gr8 tomorrow's my science exam it's truely helpful!!!!!thx soo much

• ### Abhishek Abrol Post author

Tomorrow my test and realy helpful this video

thks

• ### Boltofvolt Post author

4:00 is the 100N being applied to the 50kg box from the right or is the 50kg box moving to the right at 100N? sorry i am kinda confuse.

Get a Mac

• ### Ramvel Selvarajan Post author

in this newton's second law examples why you should not considered a negative value for force and acceleration?

• ### Jabari Morris Post author

fuck this video jp it really helped me
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• ### Frazuel Post author

Lol everyone else is watching this for tests im 11 just watching it cuz i like stuff like this XD

• ### Hei Senpai Post author

everyone here from years ago are watching this for their exam/test im just watching it for my science homework xDDD

• ### Dylan McCallister Post author

Who is here for a sanity check?

I use the tsiolkovsky equation all the time but I still need a sanity check here and there.

• ### wyskun Post author

I have a very important 2 questions for me:)

1. In space, there is a space shuttle that does't move. Mass of this shuttle is always constant. This space shuttle has a rocket engine which produce a constant force of 100N. When the engine is started and the ship has a constant thrust of 100N, when the ship starts to accelerate, will the acceleration be constant and remain constant (let's assume 10m / s), or maybe the acceleration will start to decrease as the speed increases? It is related to the rule Ek = 1 / 2mv ^ 2 ???

2. Same space shuttle doesnt move. Shuttle start to accelerate from 0km/h to 10km/h in 5 seconds and it takes "X" energy for example. How much energy it will needed to accelerate also 10km/h more in also in 5 seconds when it allready have velocity of 100km/h ? Also "X" energy? Or much more "X" of energy? And why is that?

• ### Firas Abdullah Post author

On my science book it says a=F
โโ
M