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Introduction to torque

An introduction to torque, a force that causes rotation. Understand how torque is calculated as the product of force and distance, and how it differs from work. Learn about the direction of torque and its units. Get a grasp on the concept of net torque and its role in rotational motion. Created by Sal Khan.

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  • piceratops ultimate style avatar for user Sameer
    How is torque different than Work... isnt Work formula ForceXDistance?

    Can you give an example besides Sal's?
    (89 votes)
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    • starky ultimate style avatar for user CubestormerIV
      Okay, so here I am going to assume you have a decent amount of knowledge about dimensions. Now, your confusion lies in the thinking the because both Work and Torque have the same Physical Quantities(Force and distance) being multiplied together, they must be the same. Even though both Work and Torque have the same dimensional formula ([M][L]^2[T]^2) they are not the same. Why? Because to find out Work, you multiply the Force by the Distance through which it has accelerated, and that too, using the DOT PRODUCT method, Whereas while calculating Torque, you CROSS PRODUCT the force that you apply and it's distance from the 'pivot'. I really tried mt best to explain this without a diagram. Whether you understand what I just said explained depends on how much you know about vectors and dimensions. Good Luck :-)
      (12 votes)
  • leaf green style avatar for user CheezeMaker37
    Let's say there is a stationary ruler floating in space and I apply a force to one end of it. Wouldn't it both rotate around its center of mass AND move slightly in the direction of my force? Does the movement in the direction of my force simply lessen while rotation increases, as I move farther away from the center of mass?
    (48 votes)
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    • leaf green style avatar for user Mark Zwald
      Yes, it will have both rotational and translational motion.
      Yes, as you move away from the center of mass, more energy will be put into rotation versus translation so the ruler will spin more and the COM will be displaced less.
      Good question!
      (40 votes)
  • blobby green style avatar for user Alexis Shuffler
    What exactly is torque? I know it's Force x Distance, but what does one mean when it is said "an object has torque"? From what I've found so far, the definition is pretty vague.
    (16 votes)
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    • starky ultimate style avatar for user ♪♫  Viola  ♫♪
      The others are right: torque is just another form of force. For example, Sal emphasizes that when the net torque on an object is 0, the rate of rotation remains constant. Compare this to when we said "when the net force on an object is 0, the rate of change of displacement (i.e. velocity) remains constant".

      As you see, torque is the force, rotation is circular displacement, and rate of rotation is the speed of spinning.
      (12 votes)
  • blobby green style avatar for user pei jones
    how do you calculate the force if it is not perpendicular to the turning point? i.e instead of coming in at 90 degrees its 70 degrees
    (12 votes)
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  • leaf green style avatar for user Charlie Lee
    At school, I have learnt that the equation is "Torque=Fd sin(theta)". Can I please ask when I am supposed to include angle?
    (7 votes)
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  • male robot hal style avatar for user Ananay Agarwal
    I came to this video when I was reading about gears. I mathematically understand that gears can be used to control speed and torque. But won't application of more torque just mean more acceleration and hence more speed? It just doesn't make intuitive sense.
    (6 votes)
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    • female robot grace style avatar for user cjddowd
      Gears allow you to change both the distance from the pivot point and the direction of the rotation (such as going clockwise in a vertical circle to counterclockwise in a horizontal circle). Remember, all wheels (which include gears) are 360 degree levers.
      (5 votes)
  • blobby green style avatar for user Stef Shatsky
    I am having trouble determining if the torque of the plank is counterclockwise or clockwise. like how do we determine its lever arm and its direction
    (6 votes)
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    • piceratops ultimate style avatar for user Soham Roy
      It depends on the direction of the force and the side of the pivot point or center of mass that the net force is acting upon in relationship to the viewer's eyes. If, to you the *net*force is down or closer to you on the left or up or away from you on the right of the pivot point or center of mass then the object will turn counter-clockwise. Otherwise the object will turn clockwise.
      (3 votes)
  • blobby green style avatar for user Krishna Jha
    Whats the diff b/w center of mass and center of gravity?
    (3 votes)
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    • leafers ultimate style avatar for user Ingo
      This is pretty self-explanatory and in case of a uniform gravitational field, they are the same, anyways. However, while the center of mass of a single rigid body is fixed in relation to the body, the center of gravity depends on the gravitational field, the body is in. If the field is not uniform, gravity will 'pull on' some parts of the body more, than it does on others...
      (6 votes)
  • old spice man green style avatar for user Mickey
    Hey, could one of you give an intuitive explanation of what torque is? Something that will help me better understand the concept behind torque. Torque is a measure of what? Thanks!!
    (2 votes)
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    • blobby green style avatar for user Tim Feola
      Torque is a measurement of rotational force. The force (F) is applied at a distance (d) from the pivot point. Think of loosening a tight bolt. If you have a short wrench, you would need to apply a lot of force. If you get a longer wrench and can increase the distance between where you are pushing from the bolt, it loosens much easier. The amount of torque required to loosen the bolt was always the same though.
      (6 votes)
  • blobby green style avatar for user avataratg
    So wait, what exactly is the difference between work and torque?
    (1 vote)
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Video transcript

Welcome to the presentation on torque. So, if you watched the presentation on the center of mass, which you should have, you might have gotten a little bit of a glancing view of what torque is. And now we'll do some more in detail. So in general, from the center of mass video, we learned, if this is a ruler and this is the ruler's center of mass. And if I were to apply force at the center of mass, I would accelerate the whole ruler in the direction of the force. If I have the force applying at the center of mass there, the whole ruler would accelerate in that direction. And we'd figure it out by taking the force we're applying to it and dividing by the mass of the ruler. And in that center of mass video, I imply-- well, what happens if the force is applied here? Away from the center of mass? Well, in this situation, the object, assuming it's a free floating object on the Space Shuttle or something, it will rotate around the center of mass. And that's also true, if we didn't use the center of mass, but instead we fixed the point. Let's say we had another ruler. Although it has less height than the previous one. Instead of worrying about its center of mass, let's say that it's just fixed at a point here. Let's say it's fixed here. So if this could be the hand of a clock, and it's nailed down to the back of the clock right there. So if we were trying to rotate it, it would always rotate around this point. And the same thing would happen. If I were to apply a force at this point, maybe I could break the nail off the back of the clock, or something, but I won't rotate this needle or this ruler, or whatever you want to call it. But if I would apply a force here, I would rotate the ruler around the pivot point. And this force that's applied a distance away from the pivot point, or we could say from the axis of rotation, or the center of mass. That's called torque. And torque, the letter for torque is this Greek, I think that's tau, it's a curvy T. And torque is defined as force times distance. And what force and what distance is it? It's the force that's perpendicular to the object. I guess you could say to the distance vector. If this is the distance vector-- let me do it in a different color. If this is the distance vector, the component of the force is perpendicular to this distance vector. And this is torque. And so what are its units? Well, force is newtons, and distance is meters, so this is newton meters. And you're saying, hey Sal, newtons times meters, force times distance, that looks an awful lot like work. And it's very important to realize that this isn't work, and that's why we won't call this joules. Because in work, what are we doing? We are translating an object. If this is an object, and I'm applying a force, I'm taking the force over the distance in the same direction as the force. Here the distance and the force are parallel to each other. You could say the distance vector and the force vector are in the same direction. Of course, that's translational. The whole object is just moving. It's not rotating or anything. In the situation of torque, let me switch colors. The distance vector, this is the distance from the fulcrum or the pivot point of the center of mass, to where I'm applying the force. This distance vector is perpendicular to the force that's being applied. So torque and work are fundamentally two different things, even though their units are the same. And this is a little bit of notational. This distance is often called the moment arm distance. And I don't know where that came from. Maybe one of you all can write me a message saying where it did come from. And often in some of your physics classes they'll often call torque as a moment. But we'll deal with the term torque. And that's more fun, because eventually we can understand concepts like torque horsepower in cars. So let's do a little bit of math, hopefully I've given you a little bit of intuition. So let's say I had this ruler. And let's say that this is its pivot point right here. So it would rotate around that point. It's nailed to the wall or something. And let's say that I apply a force-- Let's say the moment arm distance. So let's say this distance, let me do it in different color. Let's say that this distance right here is 10 meters. And I were to apply a force of 5 newtons perpendicular to the distance vector, or to dimension of the moment arm, you could view it either way. So torque is pretty easy in this situation. Torque is going to be equal to the force, 5 newtons, times the distance, 10. So it would be 50 newton meters. And you're probably saying, well, Sal, how do I know if this torque is going to be positive or negative? And this is where there's just a general arbitrary convention in physics. And it's good to know. If you're rotating clockwise torque is negative. Let me go the other way. If you were rotating counterclockwise, like we were in this example, rotating counterclockwise, the opposite direction of which a clock would move in. Torque is positive. And if you rotate clockwise the other way, torque is negative. So clockwise is negative. And I'm not going to go into the whole cross product and the linear algebra of torque right now, because I think that's a little bit beyond the scope. But we'll do that once we do more mathematically intensive physics. But, so, good enough. There's a torque of 50 newton meters. And that's all of the torque that is acting on this object . So it's going to rotate in this direction. And we don't have the tools yet to figure out how quickly it will rotate. But we know it will rotate. And that's vaguely useful. But what if I said that the object is not rotating? And that I have another force acting here? And let's say that that force is-- I don't know, let me make up something, that's 5 meters to the left of the pivot point. If I were tell you that this object does not rotate. So if I tell you that the object is not rotating, that means the net torque on this ruler must be 0, because it's not-- its rate of change of rotation is not changing. I should be a little exact. If I'm applying some force here, and still not rotating, then we know that the net torque on this object is 0. So what is the force being applied here? Well, what is the net torque? Well, it's this torque, which we already figured out. It's going in the clockwise direction. So it's 5-- Let me do it in a brighter color. 5 times 10. And then the net torque. The sum of all the torques have to be equal to 0. So what's this torque? So let's call this f. This is the force. So, plus-- Well, this force is acting in what direction? Clockwise or counterclockwise? Well, it's acting in the clockwise direction. This force wants to make the ruler rotate this way. So this is actually going to be a negative torque. So let's say, put a negative number here times f, times its moment arm distance, times 5, and all of this has to equal 0. The net torque is 0, because the object's rate of change of rotation isn't changing, or if it started off not rotating, it's still not rotating. So here we get 50 minus 5 f is equal to 0. That's 50 is equal to 5 f. f is equal to 10. If we follow the units all the way through, we would get that f is equal to 10 newtons. So that's interesting. I applied double the force at half the distance. And it offsetted half the force at twice the distance. And that should all connect, or start to connect, with what we talked about with mechanical advantage. You could view it the other way. Let's say these are people applying these forces. Say this guy over here is applying 10 newtons. He's much stronger. He's twice as strong as this guy over here. But because this guy is twice as far away from the pivot point, he balances the other guy. So you can kind of view it as this guy having some mechanical advantage or having a mechanical advantage of 2. And watch the mechanical advantage videos if that confuses you a little bit. But this is where to torque is useful. Because if an object's rate of rotation is not changing, you know that the net torque on that object is 0. And you can solve for the forces or the distances. I'm about to run out of time, so I will see you in the next video.