Slide – What is Torque?

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What is Torque? #1/3 Rotation and Torque

00:00
Hi everyone, today we are going to be learning about torque. Now the thing about motors and generators, which is, of course, the name of the module, is that both of these are devices that rotate in the same way that a Ferris wheel rotates. The thing is, if we are trying to rotate something like a motor, or a generator, or a Ferris wheel, we do not want the whole thing to move up or down or left to right or photo backwards, we want it to turn. And we have learned plenty about forces, which are what cause movements left and right and up and down, and forward and back. But we have not ever talked about forces, how forces can cause the turning of an object.
00:41
So, if we are going to need a new quantity called torque. And that is what causes a Ferris wheel, or a motor or generator to spin. So, motors and generators are both devices that rotate right, around some central axis when they are in operation. So far, we only know how to talk about straight lines, right? Velocity, acceleration, displacement, we did not talk about the turning of objects, until now.
01:15
So, we need a new quantity, a new thing, like force or acceleration or velocity, in order to describe the turning effect of a force, otherwise known as the turning moment. So, the force that turns an object is called torque. Right. Its magnitude is going to be proportional to the force that creates it, but it is not the same thing as a force.
01:44
Remember that force causes motion, that is moving left or right, it causes displacement and acceleration. But torque does not, torque causes rotation, it causes things like angular velocity or angular momentum. So, the torque is not only dependent on the force that created the torque, but also on where it applies to the object being turned.
02:17
So, we can imagine a spanner turning a bolt, right, this is the thing that turns so we can use it as a fantastic example to understand the talk. We can see that if we hold a spanner very far from the pivot point, it is quite easy to turn the spanner but if we hold the spanner very, very close to the pivot point, it will be almost impossible, especially if we're applying the force right on top of the pivot point. Right, that is not going to cause turning.
02:50
So obviously, the distance between the pivot point and where we push on the spanner is going to make a difference to how much turning moment or talk it can produce. So, torque is proportional to the distance between the point of application of the force and the pivot point that the object is turning around. So, we can say torque, represented by tau (τ), a Greek letter equals d times F, where F is the magnitude of the force.

What is Torque? #2/3 Direction of Torque

00:00
So, we can classify torque as clockwise or anti-clockwise, depending on which direction they're going. Right? We can talk about anti-clockwise torque being positive, and clockwise torque as negative, just as a convenient convention. Right.
00:22
Now, first, this might seem a little confusing, but remember that if we're ever talking about angles in mathematics, we can often talk about them as part of a circle. And if we were to draw a circle around here, and say that going straight across zero, then when we increase the angle, we can talk about raising up the thing like that. So, going anti-clockwise is positive torque. Right?
00:55
Now, the reason that we talk about them as positive and negative is because we're able to add them together. And having them positive and negative makes that a little easier to do. If we're talking about the direction.
01:12
The net torque of an object you see is the sum of all the talks acting on it. So, if we have one talk, turning a spinner in one direction, and another talk trying to turn the spin and back in the other direction, then we can add them together and see the torques are going to cancel out.
01:29
On the other hand, if we have two different talks, pushing a spanner in the same direction, then the net torque on that spanner will be greater than either of the individual torques. So clockwise and anti-clockwise torques will cancel each other out. And this is why we can treat them as positive and negative. Because positive and negative numbers, just like clockwise and anti-clockwise torques will cancel each other out.
01:56
We can see an example of two torques cancelling each other out in this photograph over here. If the torque on one side of the barbells was greater than the whole set of barbells would sort of start to rotate and fall down to one side, assuming we held them right in the middle. But because there's equal torque from both the right side and the left side, the net torque on the weight is absolutely zero, so it doesn't turn left or right. It just moves in a straight line. And in fact, it would travel straight down if it weren't being held up.
02:38
So, I'll just repeat it again. Torque and force are not the same things. Torque causes objects to turn or rotate and force causes objects to move. So, force is measured in Newtons, but torque is measured in Newton meters. Because we calculate Newton by– we calculate torque by multiplying a force in Newtons by distance in meters.
03:10
So, a force can only produce a torque when it is perpendicular to the axis of rotation. That means that if we take a spanner and we try to push it forward toward the axis of rotation is not going to turn. So, this will be an important property of talk when we talk about motors and generators and how they can turn.

What is Torque? #3/3 Practice Questions

00:00
Question six: consider a pendulum in motion. Which of the following does the pendulum experience?
00:08
Well, let's just draw a pendulum to start with. We have a pivot point. And we have a little mass on the end, which is swinging back and forth. So does the pendulum experience, force but not torque, torque but not force, neither force nor torque, nor both force and torque?
00:32
Let's go through these, does it experience force but not torque? Well, the problem with this is that it's rotating on its axis. Right? It's moving, left and right and sort of rotating as it does so. So, it has to be experiencing some sort of torque.
00:51
Part B, then it experiences torque, but no force. Well, that's problematic as well, because remember, the pendulum experiences a gravitational force. Without the gravitational force, there's no torque that will cause it to swing back and forth. Right.
01:07
So, it can't be B. So, it must experience both force and torque. Because you can't have rotation without a torque. And you can't have torque without a force. So, in the case of a pendulum, the force that causes the torque is the gravitational force acting on the pendulum.
01:30
Question seven: what are the units of torque? Remember, they're not Newtons, Newtons of force which causes movement. We're looking at torque, which causes rotation. So, to find talk, we take the force, and we multiply it by the distance between the force and the pivot point. So, if multiplying a force by distance, we can answer in, that's right. Newton meters. So, the torque of the object is the product of a force and the distance.
02:05
Question eight: A spanner has 100 Newtons of force exerted on it by a frustrated worker, what is the torque exerted by the spanner if the force is applied 20 centimetres from its axis of rotation. So, if we were to draw a diagram that might look something like this, we have a bolt, a spanner. 100 Newtons of force, which is enough to lift about 10 kilograms give or take. And we have 20 centimetres of Spanner or 0.20 meters. Right.
02:47
So how do we calculate torque again? Well, it's a pretty simple formula. Tau (τ), that is torque equals d times F. In this case, d is 0.20 meters, and F is 100. Newton's, right? So, multiply them together, we have 0.020, or 0.20, rather, times 100 Newtons, which gives us 20 Newton meters.
03:19
Question nine: two children sit on a seesaw. Alice is two meters from the centre and weighs 316 newtons, Bob it's 1.7 meters from the centre and weighs 400 newtons. Which direction does the seesaw go?
03:33
Now, if you're younger, and you have a plate on seesaws, you'll know that if you sit further from the middle of the seesaw, then you will have a bigger effect on the seesaw then if you sit very close to the middle. And in fact, if you have two kids of different weights, you can still get the seesaw to balance by sitting different distances from the middle. Right. So that's what this question is asking you about here. What we should look at is the torque produced by each child, and then figure out which torque is greater. And that will tell us which direction the seesaw goes.
04:04
So, let's start with Alice, alphabetical order, why not? So, Alice's torque is d times F, d being the 2.0 and F being 360 Newtons. So that'll end up as 2.0 times 360, which gives us a torque of 720 Newton meters. So, this will be the torque of the seesaw in Alice's direction. All right, what about Bob, once again, we use tau (τ) equals distance times force. Substituting in 1.7, and 400 Newtons, we end up with this expression, which evaluates to 680 Newton meters. So that's the torque in Bob's direction. So which torque is greater?
04:57
Well, we can see that even though Bob produces a larger force on the seesaw, Alice produces a larger torque. And what this means is that most of Alice's torque is cancelled out by Bob's torque. But the net torque on the seesaw is still in Alice's direction. So, Alice is the one that is at the end of the seesaw that tilts down.
05:27
Question ten: a certain bolt requires a torque of 18 Newton meters before it will come loose. But you don't want to exert more than 50 Newtons. So, how long does the spanner turn the bolt has to be? Remember, if we have a longer handle, we can produce greater torque. So, how would we figure this one out?
05:50
The thing is, we have a measure of torque already. So that's not what we're trying to calculate. We also have a measure of force, what we want is the distance, the distance of the force from the pivot point.
06:05
So, rearranging the equation, we see that the magnitude of the distance to the pivot point is going to be the torque divided by the force. Right, and we'll have to push right at the end of the spanner. If it were longer than this, then we could still push the same distance from the pivot point. But in that case, we would be using less than 50 Newtons.
06:31
So, our answer here is going to be a minimum value for the length of the spinner. If it's longer than we can still turn the bolt without exerting more than 50 Newtons. So, substituting in 50 Newtons and 18 Newton meters, we end up with 18 Newton meters over 50 Newtons, which is the same as 0.36 meters. Of course, this is a little clunky, if we're going to be talking about a spanner that is 0.36 meters long, so it might turn that into centimetres, the spanner has to be at least 36 centimetres long. If it's even longer than that, then the bolt will be even easier to turn. Right. But 36 centimetres is quite long already. So perhaps that would be a good size.
07:19
All right, so that's the end of the questions. In this section, we've looked at torque, that is the turning moment of a force, and we've seen how to calculate it. Later. This will become very useful when we talk about the torque produced by an electric motor.