Introduction to Torque Video

By: Guest More than a year ago

how can i download and save a copy of videos here?

Reply to this Comment

By: Guest More than a year ago

the vedeo are fentastic and i will lear from it.

Reply to this Comment

Introduction to Torque

Welcome to the presentation on Torque. So, if you watch 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 a little more detail. So in general, from the center of mass video, we learned that if this was a ruler and this is the ruler center of mass and if I were to apply a force at the center of mass, I would just shift the whole ruler in the—or I would accelerate the whole ruler in the direction of the force. If I had the force applying at the center of mass there, the whole ruler would accelerate in that direction and we’d figured out by digging the force that we’re applying to 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, it’s on the space shuttle or something, it will rotate around the center of mass. And that’s also true if we didn’t use a center of mass but instead we fix the point. So, let’s say we had, let’s say here’s another ruler although it has less height than the previous one. Instead of worrying about the center of mass, let’s say that it is just fixed at a point here. Let’s say it’s fixed here so it’s like I don’t know, this could be like the hand of a clock and it’s nailed down to the back of the clock right there. So, if we were to try 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 at 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 were to 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 the Torque. And torque, the letter for torque, is this Greek? I think that’s tower. 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, right. If this is the distance vector, the component of the force is perpendicular to this distance factor 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 sound, Newton’s times meters, force times distance, that looks an awful lot like work.” And it is very important to realize that this isn’t work and that’s why we won’t call these jewels because in work, what we are doing? We are translating an object. If this is an object and I am applying a force, I think the force over a distance that’s in the same direction is the force, right. Here the distance and the force are parallel to each other. You could say that the distance vector and the force vector are in the same direction. And of course that’s translational, the whole object is just moving, it’s not rotating or anything. And the situation of Torque, the distance vector, this is the distance form 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 eventhough their units are the same and this is a little bit of a 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 new message saying where it did come from? And often in some previous class, the last often called 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, right. So, we’d rotate around that point. It’s nailed to the wall or something. And let’s say that I apply a force. Let’s say that the moment arm distance so let’s say that this distance right here is 10 meters and I were to apply a force of five Newton’s perpendicular to the distance vector or to the 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 five Newton’s times the distance 10. So, it would be 50 Newton meters and if I were saying, well so 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. Well, let me go the other way, if you’re rotating counter clockwise like we are in this example, right, we’re rotating counter clockwise 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 now, I’m not going to go into the whole Physics, the whole cross product and the linear algebra of Torque right now because I think that’s a little bit beyond this scope. But we’ll do that once we do more mathematically intensive Physics. So, good enough, there’s torque of 50 Newton meters and that’s all of the Torque that’s acting up this objects. So, it’s going to rotate in this direction and we don’t have the tools yet to figure out I guess how quickly will it rotate but we know a little rotate and that’s vaguely useful. But 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 five meters to the left of the pivot point. This is five meters to the left of the fifth point. And if I were to tell you that this object does not rotate so if I tell you that that object is not rotating, that means that the net Torque on this ruler must be zero because 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 force, the net Torque on this object is zero. So, what is the force being applied here? Well what is the net Torque? Well, this Torque if you already figured out and it’s going in the clockwise direction so it’s five, five times 10. And then the net Torque, the sum of all the Torques have to be equal to zero. 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 counter clockwise? Well, it’s acting in the clockwise direction right. 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 so times five and all of this has to equal zero. The net Torque is zero because the object—its rate of change in rotation isn’t changing or if it started of, not rotating, it’s still not rotating. So here, we get 50 minus five F is equal to zero. That’s 50 is equal to five F, F is equal to 10 and if we followed 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 a distance and it offset it half the force at twice the distance and this should all connect or start to connect with what we talked about with mechanical advantage, right. You could view it the other way if these are people applying these forces. This guy over here, he’s 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 two. And watch the mechanical advantage videos, if that confuses you a little bit. But this is where Torque is useful because if an objects rate of rotation is not changing, you know that the net Torque on that object is zero and then 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.

Khan Academy

The Khan Academy is a not-for-profit organization with the mission of providing a high quality education to anyone, anywhere.

http://www.khanacademy.org/

Welcome to the presentation on Torque. So, if you watch 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 a little more detail.

So in general, from the center of mass video, we learned that if this was a ruler and this is the ruler center of mass and if I were to apply a force at the center of mass, I would just shift the whole ruler in the—or I would accelerate the whole ruler in the direction of the force. If I had the force applying at the center of mass there, the whole ruler would accelerate in that direction and we’d figured out by digging the force that we’re applying to 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, it’s on the space shuttle or something, it will rotate around the center of mass. And that’s also true if we didn’t use a center of mass but instead we fix the point. So, let’s say we had, let’s say here’s another ruler although it has less height than the previous one. Instead of worrying about the center of mass, let’s say that it is just fixed at a point here. Let’s say it’s fixed here so it’s like I don’t know, this could be like the hand of a clock and it’s nailed down to the back of the clock right there. So, if we were to try 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 at 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 were to 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 the Torque. And torque, the letter for torque, is this Greek? I think that’s tower. 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, right. If this is the distance vector, the component of the force is perpendicular to this distance factor 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 sound, Newton’s times meters, force times distance, that looks an awful lot like work.” And it is very important to realize that this isn’t work and that’s why we won’t call these jewels because in work, what we are doing? We are translating an object. If this is an object and I am applying a force, I think the force over a distance that’s in the same direction is the force, right. Here the distance and the force are parallel to each other. You could say that the distance vector and the force vector are in the same direction. And of course that’s translational, the whole object is just moving, it’s not rotating or anything.

And the situation of Torque, the distance vector, this is the distance form 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 eventhough their units are the same and this is a little bit of a 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 new message saying where it did come from? And often in some previous class, the last often called 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, right. So, we’d rotate around that point. It’s nailed to the wall or something. And let’s say that I apply a force. Let’s say that the moment arm distance so let’s say that this distance right here is 10 meters and I were to apply a force of five Newton’s perpendicular to the distance vector or to the 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 five Newton’s times the distance 10. So, it would be 50 Newton meters and if I were saying, well so 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. Well, let me go the other way, if you’re rotating counter clockwise like we are in this example, right, we’re rotating counter clockwise 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 now, I’m not going to go into the whole Physics, the whole cross product and the linear algebra of Torque right now because I think that’s a little bit beyond this scope. But we’ll do that once we do more mathematically intensive Physics.

So, good enough, there’s torque of 50 Newton meters and that’s all of the Torque that’s acting up this objects. So, it’s going to rotate in this direction and we don’t have the tools yet to figure out I guess how quickly will it rotate but we know a little rotate and that’s vaguely useful. But 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 five meters to the left of the pivot point. This is five meters to the left of the fifth point. And if I were to tell you that this object does not rotate so if I tell you that that object is not rotating, that means that the net Torque on this ruler must be zero because 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 force, the net Torque on this object is zero.

So, what is the force being applied here? Well what is the net Torque? Well, this Torque if you already figured out and it’s going in the clockwise direction so it’s five, five times 10. And then the net Torque, the sum of all the Torques have to be equal to zero. 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 counter clockwise? Well, it’s acting in the clockwise direction right. 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 so times five and all of this has to equal zero. The net Torque is zero because the object—its rate of change in rotation isn’t changing or if it started of, not rotating, it’s still not rotating. So here, we get 50 minus five F is equal to zero. That’s 50 is equal to five F, F is equal to 10 and if we followed 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 a distance and it offset it half the force at twice the distance and this should all connect or start to connect with what we talked about with mechanical advantage, right. You could view it the other way if these are people applying these forces. This guy over here, he’s 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 two. And watch the mechanical advantage videos, if that confuses you a little bit. But this is where Torque is useful because if an objects rate of rotation is not changing, you know that the net Torque on that object is zero and then 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.

Transcription by: Scribe4you Transcription Services