# Torque, Levers, and the Universal Law of Rotation

We can cause this rectangle to rotate by applying a force at this location. If we apply a force at this other location, then the rectangle will rotate in the opposite direction. If we apply a force here at the axis of rotation, the rectangle won’t rotate in either direction, since it does not know in which direction to turn. The further away from the center a force is from the axis of rotation, the more the force will cause the rectangle to turn. The same thing is true for all objects. If we apply two forces of equal strength causing the rectangle to rotate in opposite directions, then the force that is further away from the axis of rotation will win out. In order for the two forces to balance, the force which is closer to the axis of rotation needs to be of a greater strength. But, if the weaker force moves even further away from the axis of rotation, it will win out again. This is why a lever allows us to lift objects that would otherwise be far too heavy to lift with our bare hands. If we are allowed to change where our axis of rotation is located, then the point at which the effects of all the gravitational forces would cancel out, and cause no net rotation, is what we call the object’s center of mass. If an object is in space with no fixed axis of rotation, then the object will rotate around its center of mass. The center of mass does not necessarily have to be a point on the object. The total motion of an object through space is the path followed by its center of mass, plus the rotation of the object around the center of mass. A force on the object can simultaneously change both the path of the center of mass, and the object’s rotation around its center of mass. The path of the center of mass is affected by the sum of all the forces on an object, regardless of where on the object the force is applied. Where on the object the force is applied is important only with regards to how it will change the object’s rotation. All the forces on the object affect the center of mass’s path through space. But, not all the forces will affect an object’s rotation. The forces that are applied to an object can be represented as an arrow, with the strength of the force represented by the length of the arrow. This arrow can be thought of as the combination of smaller arrows which are 90 degrees to each other. This smaller arrow is the only portion of this force that contributes to changing the rotation of the object. Therefore, the how much a force affects the rotation of an object depends on the direction of the force, in addition to the force’s strength, and where the force is located. The total amount by which a force affects the rotation of an object is a combination of all these three factors, and we refer to this as the torque. The torque can be represented by an arrow. The direction of the arrow indicates the axis around which the torque is trying to rotate the object. The length of the arrow indicates the strength of the torque. If there are multiple forces acting to cause an object to rotate, then the torques produced by these forces add together. In addition to the strength and direction of the torque, there is one other factor that determines how much the rotation of an object is affected. This is how much mass is present, and how the mass is distributed throughout the object. Just as it is harder to lift an object on a lever if it has more mass Or if the mass is further away from the axis of rotation, It is similarly harder to change the rotation of an object if it has more mass, Or if the mass is further away from the axis of rotation. If an object has more mass, or if the mass of the object is further away from the axis of rotation, we give this a name, and we say that the object has a higher “moment of inertia.” The rate at which an object’s rotation changes is the strength of the torque divided by the object’s moment of inertia. The rate at which an object’s rotation changes is what we call the angular acceleration. In the case of linear motion through space, the linear acceleration of an object is the strength of the force divided by the mass. The equation for angular acceleration is very similar to this. Acceleration is replaced with angular acceleration. Force is replaced with torque. And mass is replaced with moment of inertia. The angular acceleration is the torque divided by the moment of inertia. In the case of linear motion, the speed and direction of an object is what we refer to as velocity. In the case of rotation, the speed and direction of rotation is what we refer to as angular velocity. In the case of linear motion, an object’s mass multiplied by its velocity is what we refer to as the object’s momentum. In the case of rotation, we have a similar equation. Velocity is replaced with angular velocity. As before, mass is replaced with moment of inertia. And momentum is replaced with a new term, called angular momentum. Changing how far away a mass is from the axis of rotation changes the object’s moment of inertia and it changes the object’s angular velocity. But, since the angular momentum is the angular velocity multiplied by the moment of inertia, the angular momentum stays constant. In the absence of an external torque, the angular momentum of an object is always constant. This is the same way that in the absence of an external force, the momentum of an object always stays constant. Since there are no external forces and no external torques acting on the entire Universe as a whole, this means that both the momentum and the angular momentum of the entire Universe as a whole is always constant. Much more information about the laws of motion is available in the other videos on this channel, and more videos will be coming soon.

## 100 thoughts on “Torque, Levers, and the Universal Law of Rotation”

• ### Manoj Suresh Post author

Thank you. Great work!

• ### demetris Post author

I've been searching for such a video about torque for a very long time. Thanks a lot!

• ### Butho Khan Post author

Does analysis of bending moment in concrete beams use the same concept that you showed  here.  I see similar concpets.

• ### rahul singh Post author

please prepare a video on entropy and enthalpy

• ### Pedro Kremer Post author

Nice video. Could please tell me the name of the beggining song?

• ### Zhou Wu Post author

I like the dog and the fox and the wolf. 😀

• ### Zhou Wu Post author

The frogs and the turtle are so cool!

• ### kosupuresukeba Post author

Music massacre

• ### Daniel Kostov Post author

great videos. liked and subbed

• ### Samin Kalhor Post author

best youtube channel ever…u changed my POV soooooo dramatically..Thanks

• ### CamNoble Post author

Hey Eugene. I really enjoyed this explained in simple terms. Great Video!

• ### Humberto Bustos Guzmán Post author

Clever and clear topics.

• ### Virusnzz Post author

I'm still struggling to understand something intuitively. Before I thought I did but I hadn't thought about it enough.

If you have two weights on a see-saw, why is it one can cause the other to move upwards just by being further from the axis of rotation? Aren't they both applying an equal force? I understand the centre of mass has moved, I just don't understand why the centre of mass matters. Same for the wheel. No matter where on the left side I might push down, pushing the same amount feels like it should cause the same amount of movement, no matter where you push, as long as it is in the right direction.

Can someone explain this to me?

Thnku

• ### Jan Czajkowski Post author

What is the music pl0x.

• ### Jan Czajkowski Post author

what's the music at 15:30 ;]

• ### Sean Thrasher Post author

could you say that the Torque is the change in angular momentum over change in time?

• ### iulian Post author

TY for the video , i realy appreciate

• ### Derek Dilger Post author

I wish I were good at this stuff.

• ### yashasvi2 Post author

you are the best.

• ### Michael Harris Post author

Your videos are absolutely brilliant and totally necessary for the general public who can't all be scientists but really want to understand the concepts. I can get used to the terms of angular momentum and many others and still have time for other things and to think.

• ### Bill Nye Post author

what's the name of this song?

Tight

• ### Ved Gumaste Post author

Really awesome video! Understood the concept of Moment of Inertia which I mugged up for exams! I really thank you for such great and informative videos which are helping lots of people for understanding concepts easily!😊

• ### RAMA LINGAM SARAVANAN Post author

Excellent You are rocking

• ### Kyra Bernal Post author

Can you do a video on how waves work?

• ### SixSixSix Post author

Really awesomely great, per usual !
Thanks for the brilliant work.

• ### Meloetta Kawaii Post author

lol at the fox

• ### Mainul Hasan Post author

thank You Lot

• ### Anh Đặng Linh Post author

this video is awesome

• ### peter schiller Post author

Regarding this video, the Moons rotationcenter is not the Earth, but somehow between Moon and Earth. And Earth is rotating around this rotationscenter too. So Earth and Moon rotate each other with a different radius. And the same with Sun and Planets. ^^

• ### Kelvin Kersey Post author

it's really not 'explaining' anything is it? It runs through the conventions and barks out the textbook, but it doesn't explain. It's not good teaching, it's pretty much showing off, or revising stuff for folk who already know it

• ### kellel Post author

Insanely awesome videos.You deserve 10000 eggs and 2000 liters of milk

• ### Evan Jackson Post author

This vid is stupid

• ### Michael Carr Post author

Eugene thank you so much, these videos are incredible and I love watching them. Learning so much.

• ### vengat dev Post author

wow beautiful work

• ### Kunal Mutha Post author

omg lord of the rings nostalgia

• ### Elephant in the room Post author

These videos are like a super advanced alien race has decided to come and teach us the nature of reality, step by step, gently and nicely.  Thank you 🙂

• ### Your Waifu Sucks Post author

So theoretically if you have a lever long enough can you lift the universe?

• ### Your Waifu Sucks Post author

Also does relativity apply on this? I mean if the outer edge spins faster than the ones inside does that mean that time is slower in the outer edge?

• ### نايف الشلاحي Post author

brilliant teaching

• ### সালমান রহমান Post author

You're awesome. Thanks.

• ### Salvatore Scuderi Post author

much much more physics concepts what very difficoult is understandig your choise about animals!! lol why a dog a fox a coyote (?) and a turtle and a blue frog??

强大的物理学介绍

• ### Bronson8x Post author

These videos are awesome! I've been watching your physics videos for a couple of years now. And I'm always coming back for another round of knowledge 🙂 Thank you very, very much.

• ### Jef Wowes Post author

This is perfect! The begining with the animals is awesome. I think childrem must love it. Greeting from Czech. 🙂

• ### Atakan Yüksek Post author

Thank you very much, this is absolutely amazing for me. I love see physics like this images,videos..

• ### Al Ghifari Post author

bizzare animals

• ### Toxic Sunset Post author

imagine if these videos were in virtual reality? That's a million dollar idea. You could start a khan academy with virtual reality animated tutorials and put every university out of business

thank you !!
thank you !!
thank you !!

Sn

• ### Aaron Farish Post author

Eugene I really like your videos and have learned a lot from them but it would help if you didn't have words on the screen and just had the voice. People tend to lose attention when they have both spoken and written words simultaneously.

• ### harsh singhal Post author

How do we know that no force and torque is acting on the universe?

those animals look so relaxed, i want to be like em just for a week

• ### Waltênio de Bessa Mendes Post author

Great videos! Source for knowledgment. Congratulations, go ahead.

• ### Kmal Nasef Post author

you are a genius

• ### Manuel Kuehner Post author

Great videos! What are the software tools you use for them?

• ### Nothing Post author

Nevermind any of that, I think we need to worry more about these super-wolves that have apparently figured out how to use tools and make machines.

• ### Needa khan Post author

hey eugene im a big fan of your vedios from india …..these r superbbbbbbb brilliant they r just incomparable plzzz make more n more vedios

• ### Subramaniam G Post author

Good explanation Eugene sir

• ### Mayank Singh Post author

The frogs are quite abusive in nature but fabulous explanations

• ### kumar banjara Post author

Thank you so much buddy!

• ### Eric Hiatt Post author

Is it known with absolute certainty that the angular momentum of the Universe as a whole is constant? I would guess we can't say that.

• ### Johnny Vinje Post author

15:58 : In the absence of an external torque, the angular momentum of an object is always constant. Yes out in space, but here on mother earth we have something called gravity and there is some air resistance that will slow down the object that is rotating. The angular veloctity is time dependent, and will slow down due to the friction we have in the air.
Nice videos, i have been struggling to understand the dynamics in class, but you have opened my eyes. Keep up the good work 🙂

🖒

• ### Johan Widén Post author

It would be good if conservation of angular momentum using a string through a tube could be illustrated: http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html The "unexpected" thing is that we have a quadratic factor: r squared or angular velocity squared.

• ### James Carmody Post author

10:00 I stood up and spun with the torques. My bro comes in and asks what I’m doing.

I say “I’m applying an upward torque.”

Now I get the right hand rule!

• ### Marek Małecki Post author

Please, make a movie about the moment of inertia, mass moment of inertia.

How to visualize a m^2 m^3 m^4 ?? like your movie(11:57 / 16:57)

on this site : http://www.amesweb.info/SectionalPropertiesTabs/Mass-Moment-Inertia-Hollow-Cylinder-Shaft.aspx
Mass moment of inertia Z axis is 312500 g*mm^2 (How to visualize it???)

• ### Alper Sünter Post author

It is perfect! Whenever I feel a that I forgot something, these videos are always enough.

• ### JEFFDOG Post author

THANK YOU FOR THIS VIDEO.!!!!!!!!!!!!!!!!!!!! AM=AV*MI

• ### victor sanchez Post author

Apartir de que empecé a ver estos vídeos entendí mucho mejor la física. Están fabulosos.

• ### محمد موعد Post author

What a great video .
Amazing illustration and a huge effort .
I highly appreciate your work .

• ### Abe Gamb Post author

thanks eugene

• ### Sheeba Pratap Post author

You have no idea how helpful your videos are for people in search of teachers to clear their concepts

Thank you#respect😊

• ### In love with truth truth Post author

it's really really amazing…
Yors all videos are outstanding…there are no words to describe their magnficance..
Yor are amazing….
keep it up …waiting for for new ideas and videos…

• ### Resquicios de Cielo Post author

I have to say that i like the way passion and Eugene's video style mix together to create these videos, that makes physics not only understandable but enjoyable.
As a future engineer and most important, as student i really appreciate your work, and i have to say you are clever! Grasp an abstract idea, understand it AND explain it in a way others can understand is key in education. Keep it doing. Greetings from Colombia 🇨🇴 🙂

• ### modi Maruti Post author

Great informative video sir 👍 👍 👍 great work sir

• ### utpal ghosh Post author

sir, salute to you. you are genius. this video enriched my knowledge and clear concept regarding rotational motion. we expect such more videos from you. thanks.

• ### Luis Aldamiz Post author

Philosopher dogs… that's new. XD

I still doubt the squirrel can move the moose with such a short lever.

• ### Ron Kreike Post author

Q: If the Sun would stop rotating, then why don’t the planets fall into the Sun?

• ### F_A_B123 Post author

This reminds me a lot of 2001: A Space Odyssey

• ### Kasey 1234 Post author

Your videos are the best, thanks to u i got a feel for mechanics. Subscribed!!

• ### Emilly Tábara Post author

Your videos are amazing! I appreciate all of them! it is sometimes difficult to see the behavior of the system only with pencil and paper. When I'm studying, I come to watch your videos for better understanding. Thank you for that!

• ### Physics Videos by Eugene Khutoryansky Post author

You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link:

You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately.

Thanks.

• ### wira perdana silitonga Post author

very very very good explanation

• ### shawn malbrough Post author

Thank you for your videos Mr. Eugene.

• ### Elmar Jahangirov Post author

You give a great gift to humanity. It must worth!

• ### the seeker Post author

Eugene you a brilliant person. Your way of explaining things is mind blowing.

• ### Kevin Baugh Post author

These videos are amazing!

• ### mohamed saad Post author

Great video . Anyone knows the background music please ?

• ### weylin6 Post author

For some reason, I was always under the impression that hitting something dead-on would apply more in terms of velocity, and that hitting the edge would apply more angular motion but less velocity. So no matter where you apply a force to an object, it's always the same? There's no trade-off?

• ### Blame the Social Media Post author

Made using 1st gen. Xbox graphics.

• ### Physics Videos by Eugene Khutoryansky Post author

To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available).
–To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable.
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• ### Hello HELLO!! Post author

That's not a rectangle, its a cuboid.

• ### Bill Maghan Post author

The illustrations are wonderful. Thank you for the subtitles.