Introduction to Torque An introduction to torque
Introduction to Torque
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- 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 rule, 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.
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