# Introduction to momentum | Impacts and linear momentum | Physics | Khan Academy

Welcome back. I will now introduce you to
the concept of momentum. And the letter for momentum is,
in physics, or at least in mechanics, it’s the letter P. P for momentum. And I assume that’s because the
letter M has already been used for mass, which
is I guess an even more fundamental idea. So P for momentum. So what is momentum? Well, you probably have
a general idea of it. If you see a big guy running
really fast, they’ll say, he has a lot of momentum. And if there’s a big guy running
really fast and a small guy running really fast,
most people would say, well, the big guy has more momentum. Maybe they don’t have a
quantitative sense of why they’re saying that, but
they just feel that that must be true. And if we look at the definition
of momentum, it’ll make sense. The definition of momentum is
equal to mass times velocity. So something with, say, a
medium mass and a huge velocity is going to have
a big momentum. Or something with maybe a medium
mass, but– the other way around. I forgot what I just said. So medium mass and big velocity,
huge momentum, or the other way around. Huge mass, medium velocity
would have maybe the same momentum, but it would still
have a big momentum. Or another way of doing momentum
is how little you would like to be in the way of
that object as it passes by. How unpleasant would it be
to be hit by that object? That’s a good way of thinking
about momentum. So momentum is mass
times velocity. So how does it relate
to everything we’ve been learning so far? So we know that force is equal
to mass times acceleration. And what’s acceleration? Well acceleration is just
change in velocity. So we also know that force is
equal to mass times change in velocity per unit
of time, right? Per change in time. T for time. So force is also equal
to– well, mass times change in velocity. Mass, let’s assume that
mass doesn’t change. So that could also be viewed
as the change in mass times velocity in the unit
amount of time. And this is a little tricky
here, I said, you know, the mass times the change in
velocity, that’s the same thing as the change in the
mass times the velocity, assuming the mass
doesn’t change. And here we have mass times
velocity, which is momentum. So force can also be
viewed as change in momentum per unit of time. And I’ll introduce
you to another concept called impulse. And impulse kind of means
that you think it means. An impulse is defined
as force times time. And I just want to introduce
this to you just in case you see it on the exam or whatever,
show you it’s not a difficult concept. So force times change in time,
or time, if you assume time starts at time 0. But force times change in time
is equal to impulse. I actually don’t know– I should
look up what letters they use for impulse. But another way of viewing
impulse is force times change in time. Well that’s the same thing as
change in momentum over change in time times change in time. Right? Because this is just the
same thing as force. And that’s just change
in momentum, so that’s impulse as well. And the unit of impulse
is the joule. And we’ll go more into
the joule when we do work in all of that. And if this confuses you, don’t
that you realize it’s mass times velocity. And since force is change in
momentum per unit of time, if you don’t have any external
forces on a system or, on say, on a set of objects, their
combined, or their net momentum won’t change. And that comes from
Newton’s Laws. The only way you can get a
combined change in momentum is if you have some type of net
force acting on the system. So with that in mind,
let’s do some momentum problems. Whoops. Invert colors. OK. So let’s say we have a car. Say it’s a car. Let me do some more interesting
colors. A car with a magenta bottom. And it is, let’s see, what
does this problem say? It’s 1,000 kilograms. So
a little over a ton. And it’s moving at 9 meters
per second east. So its velocity is equal to 9 meters
per second east, or to the right in this example. And it strikes a stationary
2, 000 kilogram truck. So here’s my truck. Here’s my truck and this is
a 2,000 kilogram truck. And it’s stationary, so
the velocity is 0. And when the car hits the truck,
let’s just say that it somehow gets stuck in the truck
and they just both keep moving together. So they get stuck together. The question is, what is the
resulting speed of the combination truck and car
after the collision? Well, all we have to do is
think about what is the combined momentum before
the collision? Well let’s see. The momentum of the car is going
to be the mass times the car– mass of the car. Well the total momentum is going
to the mass of the car times the velocity of the car
plus the mass of the truck times the velocity
of the truck. And this is before they
hit each other. So what’s the mass of the car? That’s 1,000. What’s the velocity
of the car? It’s 9 meters per second. So as you can imagine, a unit of
momentum would be kilogram meters per second. So it’s 1,000 times 9 kilogram
meters per second, but I won’t write that right now just to
keep things simple, or so I save space. And then the mass of
the truck is 2,000. And what’s its velocity? Well, it’s 0. It’s stationary initially. So the initial momentum of the
system– this is 2,000 times 0– is 9,000 plus 0, which
equals 9,000 kilogram meters per second. That’s the momentum before
the car hits the back of the truck. Now what happens after the car
hits the back of the truck? So let’s go to that situation. So we have the truck. I’ll draw it a little
less neatly. And then you have the car and
it’s probably a little bit– well, I won’t go into whether
it’s banged up and whether it released heat and all of that. Let’s assume that there was
nothing– if this is a simple problem that we can do. So if we assume that,
there would be no change in momentum. Because we’re saying that
there’s no net forces acting on the system. And when I say system, I
mean the combination of the car and the truck. So what we’re saying is, is
this combination, this new vehicle called a car truck, its
momentum will have to be the same as the car and the
truck’s momentum when they were separate. So what do we know about
this car truck object? Well we know its new mass. The car truck object,
it will be the combined mass of the two. So it’s 1,000 kilograms plus
2,000 kilograms. So it’s 3,000 kilograms. And now we can use
that information to figure out its velocity. How? Well, its momentum– this
3,000 kilogram object’s momentum– has to be the same
as the momentum of the two objects before the collision. So it still has to be 9,000
kilogram meters per second. So once again, mass
times velocity. So mass is 3,000 times
the new velocity. So we could call that, I don’t
know, new velocity, v sub n. That will equal 9,000. Because momentum is conserved. That’s what you always
have to remember. Momentum doesn’t change unless
there’s a net force acting on the system. Because we saw a force is change
in momentum per time. So if you have no force
in it, you have no change in momentum. So let’s just solve. Divide both sides of this by
3,000 and you get the new velocity is 3 meters
per second. And that kind of makes sense. You have a relatively light
car moving at 9 meters per second and a stationary truck. Then it smacks the truck
and they move together. The combined object– and it’s
going to be to the east. And we’ll do more later, but we
assume that a positive velocity is east. If somehow we
ended up with a negative, it would have been west. But it
makes sense because we have a light object and a stationery,
heavy object. And when the light object hits
the stationery, heavy object, the combined objects still keeps
moving to the right, but it moves at a relatively
slower speed. So hopefully that gives you a
little bit of intuition for momentum, and that was not too
confusing of a problem. And in the next couple of
videos, I’ll do more momentum problems and then I’ll introduce
you to momentum problems in two dimensions. I will see you soon.

## 100 thoughts on “Introduction to momentum | Impacts and linear momentum | Physics | Khan Academy”

1. iii. hxe says:

A cartruck now we have a new vehicle HAHAHAAH i laughed more than i should on this

2. Christina DC says:

Thanks for video ,Sir. It's good, but I didn't get you, when you said that;" if there is no force there is no change in momentum" .Ya, it's absolutely right .

But the one more thing you have done was you had used the same value of momentum as before (while truck was at rest), but if the car strikes the truck doesn't it giving a pushing force to the truck and even the momentum is same???

I hope you will reply it in a comprehensive way. Thanks!!!

Regards,
Christina 🙂

3. Glen Gaming says:

why is the quality stuck at 240p?

4. Mansi Thareja says:

u r the best..ur all tutorials are so helpful. thankyou so much😙😙

5. Chiara B says:

Can't believe they're actually naming momentum as "p" and electric potential as "V". It's completely unrelated.
Why didn't they just named mass as a small 'm' and the momentum as capital 'M' ?

6. Pozmitive says:

so force is the rate of change of momentum

7. Ein Hacker-Typ says:

Pretty useful, thanks!

8. Pro_Di_Jai 321 says:

9. Joao Barbot says:

thanks for the video. very useful. What is the black board sofware?

10. ALEF COIMBRA says:

Great video! It helped me a lot. Thank you very much.

11. Andres Salcedo says:

Really helpful, this will definitely help me on my test tomorrow.

12. Anshul Mohan says:

"CarTruck" LOL

13. tenton2000k says:

What grade in the US is this concept taught? im curious. learning this for the first time in calculus based university physics.

14. Talia says:

I take physics as a Freshmen… is that weird ?

15. Pixicandy l says:

Can anyone tell me why he added 0 to 1,000kg times 9. Is it just a placement number or is he adding the velocity from the truck as well?!

16. RobertoEmilioRomero says:

@ 3:28, THe Unit of Impulse is "The Joule" ?? Is that what he said? Isn't it kgm/s or the N*s??

17. Santosh Mukherjee says:

18. Jerika Nagal says:

How did you get that new velocity of 3m/s?

19. Labib Mohammed says:

Thank You 😊! It will help a lot in my exam tomorrow!

20. The Pimp says:

Thats Awesome i have a life that i dont understand this , thanks god , finally , Khan Academy thanks !

21. mr robert says:

But then the equation E^2=(mc^2)^2 + (pc)^2 cannot explain light since it has no mass

22. Theo Volz says:

23. Danielson Correa says:

thank you very much

24. G.D studio GL says:

thankyou its really helpful you deserve a like👍

25. Jennifer Q says:

Letter for Impulse is "J"

… I assume that's because the letter "I" has already used for Moment of Inertia…

26. jaymes leeder says:

This video helped a lot and i have my physics final next Tuesday😭

27. shravya reddy says:

goood

28. Tyrone Kock says:

Can somoene explain when does momentum change in a system?

29. Rockswamp28 says:

Lol, I've been watching these physics videos all day and got kind of bored, so I started messing around with the speed. Sal sounds so drunk when you set the video to .5x speed.

i also have a better concept in AP physics class.

31. Farah KSP says:

is it just who prefer the old videos to new one? he just sounds sexier in the old vids XD

32. Ajay Prashant says:

I got the problem solved in just 1 second without the math.

33. Akshay Kalia says:

Waste of time

34. Johnson George says:

what is conservation of momentum?

35. catherine eskander says:

i luv p.locopolous

36. Alastair Heys says:

https://youtu.be/vGeELTahWTA

37. Steven Archuleta says:

It's important to note, I think, that this is an example of a COMPLETELY INELASTIC COLLISION, because after contact, the two objects begin moving together as a unit as though they were stuck together.

38. sumit kumar says:

My new PHYSICS SOLVING APP.More then 150+ formulas,Solves for any variable you want,Covers up all physics.download now.https://play.google.com/store/apps/details?id=com.physics.lenovo.myapplication

39. Tina Lu says:

thank you thank you thank you thank you

40. natsume the llama says:

WHAT

41. Anupam says:

http://physicsteacher.in/2017/11/18/momentum-impulse-theorem-newton/

42. Phil Fan says:

love dis!!

43. ODCOLE says:

As my highschool physics teacher for grade 11 always says, "biology isn't a science"

1:17 "how unpleasant would it be to be hit by that object" LMAO

A FOR AWESOME

46. Jithin Primz says:

impulse-J;momentum-p

47. redstone craft guy says:

Momemtum is Newton's first law like you already said before. Done, video ended.

Jk

48. theoj mandude says:

Best physics lesson ever

49. Gobind Grover says:

great job sal. its impressive that how you conceptualize and explain it..

50. Kate Ortega says:

how about ball of pool that hits together and it hits the another and another how can the equation be is it m1v1 + m1v1 = m2v2 + m2v2

51. jamesb101100 says:

Measured in juuls

52. Michelle Mustacisa says:

how to find mass and velocity using momentum???

53. Knot E says:

proud to be bangladeshi cuzz da owner of da channel has bangladeshi roots

54. Xiting Zhang says:

I hate these old videos… resolution is so low

55. sesshoumaru3st says:

Ok , so velocity = momentum/mass and mass = momentum/velocity and momentum = mass * velocity. hmm this reminds me too much of the loop distance , time , and speed seem to create because you can't have one without the other.

56. thabiso aubrey maila says:

that's awsome

57. BAYPALS says:

just curious, what year level are you learning this at school? or how old are you when you got taught this?

58. K's view says:

Thankgod there is no one to disturb on youtube like in class.

59. Jeremy Barber says:

Can anyone explain conservation of momentum

60. jaison antony says:

thank you. cleared my doubt.

61. Majd Jamous says:

This was 10 years ago

Why we take delta as a change

And what is the proof that momentum Is more for a big guy

Give derivations of formulas from where it comes and why it holds

Why the momentum should be the same when car and truck hit like it was before hitting it please explain and there can be a change of force when they get hit by each other

66. Shreyans Saklecha says:

Mass never change……

67. Johann 101 says:

wait, will the new velocity be the square root of the initial velocity before momentum started, like for the car example?

68. No No says:

If the internet had more of this and less off… that, we'd all be better off.

69. NAME: TechGuy says:

IMPULSE HAS NO UNITS

70. AnM Rivera says:

Nice 👍 thank you

71. ATMOSK1234 says:

The unit of the impulse can't be joules since joules is (kg*m^2)/s^2 and momentum is kg*m/s. Right? Impulse should be force X time, so (kg*m) since the seconds cancel out.

I was going to complain about the font but then I realised that it's a 10 years old video.

73. Fran Beltran says:

Taking this in my sophomore year of high school!!! This is so confusing…. 😩😩

74. Ahmed Rizwan says:

"new vehicle called car-truck"

75. Nimmy Tiwary says:

Allakh pandey sir( physics wallah) please also make a video on impulse and impulsive force.

76. Sofia Abel says:

HERESY!!!! joules is most certainly not the unit for impulse.

77. Reder Khalifa says:

Am I supposed to be taking physics in 9th grade?

78. Robert Sevik says:

like the video but maybe you should have introduced a perfect inelastic and perfect elastic collision.

79. ibrahim ismail says:

Thank you so much! Suppose the truck is moving against the direction of the vehicle, how will mathematical calculations of momentum,.

Sir which software are you using?

81. SHEILA DENUM says:

82. Nataraja D says:

I want a car cartruck

83. VIP *crown emoji* says:

I need a video where there is an actual explanation of the concept not just putting laws and etc

84. Olivia Mayers says:

I feel like I’m in the future in 2019

85. Sky Guy says:

Thanks for existing

1:18 Kinetic energy is a better representation of how unpleasant it is to be hit by an object. After a gun is fired, the gun and bullet have the same magnitude of momentum but the bullet has much greater kinetic energy.

87. Nikolay Nikolov Valkanov says:

thanks for helping, its 2019 by the way.

88. Lama says:

I love you again…. LIFE SAVER

89. Feel Physics says:

how can u prove that f=ma

90. Feel Physics says:

how can u prove that if we multiply mass and velocity of anv object then we will know how much force is required to stop that object

91. Trius says:

Does a bullet have a velocity or an acceleration and deceleration?

92. Secrets of the World says:

nice but mass have unit m not M

93. Zestamore Garcia says:

What makes change in time equal to unit in time?

94. Remarkable SeiF says:

But how does an impact on a 2000kg object not change the momentum?

P = mv

96. Rami Abolnasr says:

Unit of impulse is =J the equation is J=F•T unit Newton second (NS)

97. Hugh Jones says:

Units of impulse are NOT the Joule. Joule = units of ENERGY.
Units of impulse are the same as units of momentum because an impulse is just the change in momentum.
Units of momentum are the kg m / s ("kilogram meter per second")

98. Majd Hailat says:

3:28 joule? I thought it has the same units as momentum? Kg*m/s or N*s