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## Physics library

### Unit 7: Lesson 2

Torque, moments, and angular momentum- Introduction to torque
- Moments
- Moments (part 2)
- Finding torque for angled forces
- Torque
- Rotational version of Newton's second law
- More on moment of inertia
- Rotational inertia
- Rotational kinetic energy
- Rolling without slipping problems
- Angular momentum
- Constant angular momentum when no net torque
- Angular momentum of an extended object
- Ball hits rod angular momentum example
- Cross product and torque

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# Introduction to torque

An introduction to torque. Created by Sal Khan.

## Want to join the conversation?

- How is torque different than Work... isnt Work formula ForceXDistance?

Can you give an example besides Sal's?(89 votes)- 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 :-)(9 votes)

- 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?(45 votes)
- 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!(36 votes)

- 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.(15 votes)
- 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)

- 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(10 votes)
- The complete method for calculating Torque is actually

T(torque) = F(force) * s(distance from pivot) * sin(theta), where theta is the angle between the force and the position vector. In your question theta = 70. So you can just plug in the value to find your answer :-)(5 votes)

- At school, I have learnt that the equation is "Torque=Fd sin(theta)". Can I please ask when I am supposed to include angle?(6 votes)
- In high schools the formula is usally shown as "torque=force*distance" because we assume that there is a right angle between the force and the lever arm. The other formula is more general, and takes into account when the angle theta is not 90 degrees (sin90=1). Hope that helps.(8 votes)

- 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)
- 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)

- 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)
- 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)

- Whats the diff b/w center of mass and center of gravity?(3 votes)
- 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)

- 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)
- 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)

- So wait, what exactly is the difference between work and torque?(1 vote)
- work is when the force acting on the object is parallel and it move the object. Torque, on the other hand, is when the force acting on the object is perpendicular to the moment arm and it causes the object to swing around a point not just transitionally move.(6 votes)

## 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.