Lesson video

Hello there, I'm Mr. Forbes, and welcome to this lesson from the Forces Make Things Change unit.

This lesson's all about the turning effect of forces or moments, as we call them, and how those moments can help levers and gears operate to change the size of forces.

By the end of this lesson, you are going to be able to describe how forces cause objects to turn by producing a rotational effect called a moment.

You are also going to be able to describe how levers and gears use those turning effects to increase or decrease the size of forces.

The keywords you need to understand to get the most of the lesson are shown here.

First of them is equilibrium, and that's the state of an object when there's no resultant force acting on it.

An object is in equilibrium when there's no resultant force.

Moment is the turning effect of a force and that's measured in newton metres.

A force multiplier is a type of lever that will increase the size of a force you apply to produce a larger load force.

A distance multiplier is a lever that will increase the distance when part of the lever moves.

It decreases the force And gears are toothed wheels that rotate and transmit forces from each other.

This lesson's in three parts, and in the first part, we're going to be looking at the turning effect of a force called a moment and how that moment can be used in levers.

In the second part of the lesson, we'll be looking at how to calculate the size of that turning effect or moment.

And in the third part of the lesson, we'll be looking at how gears lock in with each other and transfer that turning effect from one place to another.

So let's start by looking at turning effects.

This diagram shows two people trying to pull a cupboard in opposite directions using ropes.

So they're pulling to the left and to the right with forces of 400 newtons.

Those forces are equal and in opposite directions and in line with each other.

The cupboard's not going to move left or right because no side is winning in that sort of tug of war and there's no resultant force on it.

And that cupboard therefore is in equilibrium.

It's going to stay stationary if it was stationary.

Now, imagine that those two forces weren't in line with each other.

So we've got the same sized forces, 400 newtons in each direction.

But this time, one of the forces is at the top and one is at the bottom.

And what will happen in this situation is, as you'd imagine, the cupboard will rotate.

It will topple over, it will tilt towards one direction, and fall to the ground, breaking everything in it.

So the pair of forces acting on the object in opposite directions but not in line with each other can create a turning effect on that object.

And we call that turning effect the moment of the force.

So there are moments acting on that cupboard and that causes it to twist or turn.

Previously we said an object is in equilibrium if there's no resultant forces on it, but we've got to extend that definition slightly now because the object is starting to do something even when there was no resultant force on it.

So an object is in equilibrium when there's no resultant force on it and there are no resultant moments.

So I've got three situations here.

I've got the first situation.

That one's not in equilibrium because the forces are of different size.

So there is a resultant force on that one.

This second one is not in equilibrium either.

Although there's a four to five newton to the left and four to five newton to the right, those forces aren't in line and that object will start to rotate.

Only the third object is in equilibrium because it's got equal size forces in each direction and they're in line with each other.

So that one is in equilibrium.

Okay, let's check if you understand our new definition of equilibrium.

In which of the following situations will the box in the diagrams start to rotate or turn? So, choose from figure A, B, or C.

Pause the video, make your selection, and restart please.

Welcome back, you should have selected C.

You can see there that you've got two forces and they're in opposite directions, and even though they're the same size, they're not in line with each other.

So they'll actually cause rotation.

So those two forces, not in line, and in opposite direction, so it's gonna rotate.

In the first figure, that box is going to stay stationary because we've got forces that cancel each other properly.

Those that are in line with each other.

And then the second box, that's gonna accelerate towards the right because both forces are pushing to the right.

So it's not gonna rotate, it's just going to accelerate to the right.

So, well done if you selected C.

We can use a pivot to cause an object to rotate when a force acts on it.

So I've got a simple metal rod here with a pivot shoulder.

And if I put a force on it, that force is going to cause that metal rod to rotate.

And it's gonna rotate like that which we describe as an anti-clockwise direction.

The other rotation is clockwise that you could have, but this one is anti-clockwise.

And that's an example of a simple lever.

Putting a force on one end causes rotation of the other end.

So to check if you understand rotation, I'd like you to select which of these diagrams correctly shows the turning of the lever caused by the applied force.

So you can see, all of the turning described there as clockwise, and it got forces in different directions.

But I'd like you to identify which one of those diagrams is correct.

So pause the video, make your decision, and restart please.

Welcome back.

Hopefully, you selected A, That lever is going to turn clockwise around the pivot, and that's what the turning arrow shows.

The second one is going to turn anti-clockwise, and so is the third one.

So that's gonna turn anti-clockwise as well.

So, well done if you selected A.

Levers are used to make objects move.

So I've got my solid lever here and my pivot, and that's the simplest type of lever, and it operates like this.

So I apply a force called the effort force to one end of the lever, and putting that effort force on that end will cause the lever to attempt to rotate, in this case, anti-clockwise.

If I put an object on the other end, a force will act on that object, and we call that force, a load force.

So putting an effort force on one end of the lever produces a load force on the other end of the lever.

Probably the simplest lever you may know of is a crowbar.

And this is an example of a lever that acts as a force multiplier.

So that's a picture of a crowbar there with a pivot at near one end and somebody pushing down at the far end.

And what happens is you put a small effort force at one end of the lever and it rotates around the pivot, and it produces a very large load force at the other end of the lever.

And that allows you to lift very, very heavy objects, only a small distance though.

So that long crowbar can lift heavy objects.

The load force is much larger than the effort force you have to put in.

There are other types of levers called distance multipliers, and distance multipliers produce large movement from very small movements.

A good example of that is the human body which contains quite a lot of distance multipliers.

So I've got a picture of the arm muscles here and the arm bones and the biceps in the arm here.

And those are muscles that can contract and produce very powerful forces, but they only contract by a very small distance, but they produce that very large force.

That gives us a very, very large effort force acting on the bones of the arm around the elbow.

So the elbow is acting as the pivot in this lever.

And the lower arm then acts as the lever and it makes the hand move through a large distance.

So a small contraction of the biceps can cause your lower arm to move through a large distance, but the force that that produces on the hand is much smaller than the effort.

So the biceps are producing a very large force in a small distance, and the hand has got a large distance, but it's only able to produce a smaller load force.

And that's a distance multiplier.

Now, as you've seen force multipliers and distance multipliers, I'd like you to decide which of these levers are force multipliers and which are distance multipliers.

So I've got four levers here.

The forces are not to scale, but the distances apart they are and the distances they are from the pivot are to scale.

So pause the video, decide which of these are force multipliers and which are distant multipliers please, and then restart.

Welcome back.

Well, lever A is a force multiplier.

The effort is a long way away from the pivot and the load is close to the pivot, so that will increase the size of the force.

B is also a force multiplier.

You've got the effort a long way away from the pivot, and the load quite close to the pivot.

So that's gotta be a force multiplier as well.

C is a distance multiplier.

The effort is very close to the pivot, while the load is much further away.

And similarly for D, that's a distance multiplier as well because the effort is close to the pivot and the load is far away.

Okay, we've reached the first task now.

And all I'd like you to do is to read through the sentences there and fill in the missing gaps please, describing different types of levers and turning effects.

And then, for question two, I'd like you to state the two conditions needed for an object to be in equilibrium now.

Remember, there are two separate conditions.

So pause the video, answer those questions, and restart please.

Welcome back, and here's the gaps filled in.

The turning effect of a force is called a moment.

A lever rotate arounds a pivot when a force is applied to one end.

A lever is used to increase the.

Sorry, a lever used to increase the size of a force is known as a force multiplier, while a lever used to cause large movements from smaller movements is known as a distance multiplier.

And the two conditions are, an object in equilibrium is in equilibrium if there is no resultant forces acting on it and there are no resultant moments.

So, well done if you got those two.

We're now gonna move on to the second part of the lesson.

And in it, we're going to calculate moments, the turning effect of those forces.

Let's start doing that.

The size of the turning effect or the moment is given by this equation, the moment is equal to force times the distance.

And you can see I put in brackets there, normal to the direction of the force.

And we'll look at what that means a bit later.

But for now, moment is force times distance.

So we can write that as M equals F times d, where M is, this is what we use for moments, and that's measured in newton metres.

F is for force and we measure that in newtons.

And D is the distance, again, normal to the direction of the force in metres.

So we'll see what that little details in brackets means a bit later.

So let's start with some simple examples.

I'm gonna calculate the moment caused by a force here, and then I'll ask you to try to do the same.

So, calculate the moment caused by the force shown in the diagram below.

And what I've got there is a pivot, and I've got a force of 7.

5 newtons acting on a lever.

And that's not 0.

4 metres away from the pivot as you can see.

So to solve that, all I need to do is to write moments is force times distance, and then I can substitute in the values that I can read off the diagram.

So the force is 7.

5 newtons and the distance is not 0.

4 metres, so I can just multiply those two together and that gives me a moment of 3.

0 newton metres.

So it's newton's times metres.

And that's going to cause that to rotate anti-clockwise.

So I've also written anti-clockwise there.

What I'd like you to do now is to calculate the moment caused by the force shown in this diagram.

So we've got a second diagram with a force and a distant and a pivot, and I'd like you to calculate the moment.

So pause the video, calculate the moment, and then restart please.

Welcome back.

Well, you should have written the equation, moment was force times distance using the symbols here.

And then substituting the values read from the diagram, and that gives us a moment of 0.

6 newton metres.

And in this case, it's a clockwise moment.

It's going to make that lever rotate clockwise.

So, well done if you got that.

Now we're gonna look at why that section of the equation was in brackets about the distance being perpendicular to the force.

So I've got a lever here, and this lever's tilted.

And I've got a force acting on it of 8.

0 newtons.

And you can see the pivot there.

But I haven't marked on the distance yet.

What I'm gonna do is mark on the direction of the force, something called the line of action of the force.

You can see I've drawn that on with that dotted purple line there.

And that line of action tells me which direction the force is acting in.

The distance we use in the equation, the distance D, is the distance perpendicular to that line of action.

So it's how far away it is from the pivot along that line of action at right angle, so this.

We draw a right angle from the line of actions of the force to the pivot, and that's the distance we use to calculate the moment.

So if I wanted to calculate the moment of this 8.

0 newton force, I'll multiply it by that distance, 0.

4 metres, like this.

Moments, force times distance perpendicular to the pivot.

You write those two values in, and we'll get a moment of 3.

2 newton metres.

Okay, I'd like you to calculate the moment caused by this force of this tilted lever.

So I've marked on all the information you need on the diagram, and I'd like you to just calculate the moment correctly, please.

So pause the video, calculate the moment, and restart please.

Welcome back.

Well, hopefully, your answer was 4.

8 newton metres.

And that's because the distance you should use in the calculation is the distance perpendicular to the line of action of the force, and that's the 0.

8 metres.

So the perpendicular distance is 0.

8 metres, not the 1.

0 metres marked along the beam there.

So we use that distance and we write out the calculation.

I've done it in words here, moment is force times perpendicular distance to the pivot.

Substitute those two values in.

6.

0 newtons times 0.

8 metres, gives a moment of 4.

8 newton metres.

Well done if you've got that.

Sometimes the force might not be at right angles to the lever itself.

So I've got a force here of 2.

0 newtons.

But you can see, it's not acting at right angles to the distance I've marked there, and I need to use the correct distance.

So what I've got to do in that case is draw the line of action of the force again like we drew earlier, and I've drawn that on as a dotted line here.

And you can see that the perpendicular distance in this diagram is now 0.

3 metres.

So it's 0.

3 metres away from the pivot.

So if I want to calculate the moment here, I calculate the distance from the pivot to the line of action of the force at right angles.

So writing the equation again, moments is force times distance.

Substituting the correct values.

It's two newtons, and it's 0.

3 metres away from the pivot.

And that gives me a moment of 0.

6 newton metres.

Now I'd like you to calculate the moment caused by a force that's not acting at right angles to the lever.

I've got the diagram here with all of the information you'll need.

So pause the video, calculate the moment caused by this force, and then restart please.

Welcome back.

And you should have found the answer is 4.

5 newton metres 'cause you're using the size of a force and multiplying it by the perpendicular distance of the pivot.

So the perpendicular distance of marked is 0.

5 metres.

So the calculation is shown there, it's 4.

5 newton metres.

Well done if you've got that.

Let's have a look at a more difficult example now where I'm using a crowbar to lift a heavy load, and I've got a force acting on that crowbar, and I wanna find out how large a load I can lift using that force.

So I've got 200 newtons acting downwards, and it's a perpendicular distance of 1.

2 metres away from the pivot.

And then, I've got a force on the other side and it's 0.

2 metres away.

So that's my load force 0.

2 metres away from the pivot.

The first thing I should do is find the moment produced by that effort force.

So I can calculate that using, moments is force times distance.

The force is 200 newtons downwards and it's 1.

2 metres away.

So I'll substitute those in.

And that gives me a moment of 240 newton metres.

What I can do next is find the load force using that moment, because the moments that you put on one end of the lever are equal to the moments on the other end of the lever.

So I can write out the equation, force is moments divided by distance.

I've rearranged the moment equation there.

I know the moments and I know the distance, so I can calculate F load, the load force.

So I substitute in the moments I've just calculated, 240 newton metres, and divide them by the distance in that pivot, 0.

2 metres there.

Doing that sum gives me a force load of 1,200 newtons.

So by putting a force of 200 newtons on one end of this lever, I can produce a load force of 1,200 newtons.

Now it's your turn to try the same sort of exercise.

I want to know what sized effort is needed to lift a load.

So I've got a load that's 2,000 newtons, it's 0.

2 metres away from the pivot, and I push down with an effort force that's 1.

6 metres away from the pivot.

I'd like you to work out what sized effort force is needed.

So pause the video, work out the effort force, and restart please.

Welcome back.

Hopefully, you selected 250 newtons.

And we'll go through the process of finding the answer.

The first thing we're gonna do is, we find the moment produced by the load.

It's 2,000 newtons times 0.

2 metres, and that's 400 newton metres.

And that means, the moment on the other side of the lever must be the same, 400 newton metres.

So I can find the effort force by rearranging the equation, force equals moments divided by distance in that case.

The moment was.

Sorry, 400 newton metres.

We divide that by 1.

6 metres, and that gives us 250 newtons.

So we can use a 250 newton effort force to lift 2,000 newtons.

Well done if you got that.

And now it's time for the second task.

And what I'd like you to do is to find the moment caused by each of the forces in these four diagrams, and I'd like you to give all your answers in newton metres please.

So pause the video, work out the size of each of the moments produced, and then restart.

Welcome back.

And the first example is the simplest.

We've got a force of 15 newtons and a distance of 0.

6 metres, and that gives us a moment of 9.

0 newton metres.

In the second case, I've got a distance to the pivot of 40 centimetres or 0.

4 metres and a force of 5.

5 newtons, multiplying those gives a moment of 2.

2 Newton metres.

Well done if you've got those two.

And now the two more difficult examples.

In this case, I've got a force of 24 newtons and it's 0.

4 metres from the pivot if you measure perpendicular to the direction of the force.

That gives me a moment of 9.

6 newton metres.

And then the final one.

Again, I've got a force of 30 newtons, and that's 5.

0 centimetres away from the pivot or 0.

05 metres.

Multiplying that together gives us 1.

5 Newton metres.

Well done if you got that.

And now we're gonna move on to the final part of the lesson, which is all about gears.

And gears are used to transfer moments from one place to another.

A gear is a toothed wheel, and it's easy to show a diagram of that.

We've got a diagram here of a complex set of gears.

And you can see that there's a series of teeth on those gears.

And the interlock, when one gear rotate, it rotates another, and it transfers the turning effect of a force.

So I've got a simplified picture of a gear here to make it easier.

And you can see, these parts of the gear are called the teeth, and the gear rotates around a central axle, a point in the middle.

So there's a point of rotation and the gears rotate.

And as you can see from the photograph, the gears interlocked with other gears, and they each cause each other to move or rotate.

So we connect gears together so that when one gear rotates, it causes another gear to rotate.

And that's best seen with a simple animation.

I've got two gears here, and the blue gear's rotating around.

And because it's intermeshed with the other gear, you can see the teeth connect to each other as it rotates, it causes that second gear to rotate.

So I'm getting one gear causing a second gear to rotate.

This first gear, it's got 12 teeth on it.

And you can pause the video and count them if you like, but there's 12 teeth there.

And the second gear has only got six teeth on it.

So as they rotate, the teeth on the first gear push on the second gear, and it cause it to rotate.

But the smaller gear has to rotate two times for one rotation of the larger blue gear here.

So watch the animation, and you can see that every time the blue gear rotates through one complete rotation, the grey gear rotates through two complete rotations.

Okay, what I'd like you to do is to work out how many times a gear rotates.

So I've got a diagram of two gears that are connected together here.

How many times does gear Y rotate? That's the smaller gear.

When gear X completes one full revolution, is it one time, two times, three times, or four times? So pause the video, work out how many rotations there'd be, and then restart please.

Welcome back.

The gear would rotate three times.

So gear Y rotates three times for every one rotation of gear X.

And the reason for that is gear X is 30 teeth and gear Y is only 10 teeth.

So if you count those gears you'll see that.

And so when gear X rotates, 30 teeth pass through the connection.

So gear Y must have 30 teeth that pass through the connection.

That must mean it rotates three times 'cause three times 10 is 30.

Well done if you've said three times.

Gears are used to increase the size of moments.

So we can use a pair of gears to generate a larger moment.

I've got a set of gears here.

And if you have a force acting on one gear, then it's gonna produce the same sized force acting on the other gear equal and opposite forces, according to Newton's third law.

So the force is the same size on both gears and we can mark that on.

I've got blue force and red force showing the forces on the two different gears.

And if those gears have different radii, the moments are going to be different produced by the teeth 'cause the force is the same, but the distance to the point of rotation is different.

So we're gonna get a different moment on the two different gears.

So the moment of the smaller gear is going to be smaller than the moment of the larger gear.

Okay, let's check if you understood what I said there.

In which of the following gear arrangements will the moment at the teeth of gear Y be smaller than the moment of the teeth of gear X? So look very carefully at the size of the gears, the diameter of the gears, and make that decision please.

Pause the video, select the correct option, and restart.

Welcome back.

The answer should be C.

Y has a smaller radius, and so smaller moment to each teeth.

In figure B, they're both the same radius, so the moment would be the same.

And in figure A, well, Y has got the larger radius so it'd have the larger moment.

So figure C was the correct option.

Well done for selecting that.

Let's have a look at a calculation we can do to find out how much the moment changed.

So I've got a set of gears here.

I've got one gear that's got a radius of 0.

3 metres and one gear that's got a radius of 0.

1 metre, and the teeth act on each other to produce a different moment.

So we've got a gear of radius 0.

1 metre, and it's producing a moment of 10 newton metres.

So we've got the size of its moment.

What we're going to do is calculate the size of the moment on the other gear.

So the force produced by the small gear can be calculated by using the moment equations, moment is force times distance.

So force is equal to moment divided by distance.

And that's 10 newton metres divided by 0.

1 metres, and that's 100 newtons.

So we've calculated the size of the force produced at the teeth of the gear.

And as we said earlier, that force is the same on both sets of teeth.

So the moment on the large gear is also the same, also involves the same force.

So the moment is the force times the distance.

So we know the moment is 100 newtons, 'cause that's the size of the force we just calculated.

And we know its diameter is 0.

3 metres, so we can calculate the moment.

And the moment on that second gear is 30 newton metres.

So what we've done is we've taken a moment of 10 newton metres and produced a moment of 30 newton metres.

We've increased the moment.

Okay, what I'd like you to do is to try out the same sort of calculation.

I've got a large gear with a radius of 0.

14 metres, and it's driven by a smaller gear with a radius of 0.

07 metres.

I'd like you to calculate the moment acting on the larger gear when the moment of the small gear is 21.

0 newton metres.

So pause the video, follow the same type of calculation I did earlier, and try and find out what that moment is.

Restart when you're done.

Welcome back.

You should have selected 42 newton metres.

Again, we follow the same stages.

We calculate the force on the teeth of the smaller gear.

Moments force times distance, so force is moments divided by distance.

And that gives us 300 newtons when we substitute the values in.

And then we use that moment in the.

Sorry, we use that force in the calculation of the moment on the larger gear.

So it's the force times the distance, and that gives us 42.

0 newton metres.

Well done if you got that.

Okay, we're onto the final task of the lesson, and what I'd like you to do is this.

I'd like you to look at the diagrams which show a set of gears X and Y, three different sets of gears though.

And in each case, gear X is rotated once.

I'd like you to work out how many times does that cause gear Y to rotate.

And then, for question two, I've got a pair of gears there with some radiuses.

And what I'd like you to do is to use the data provided to calculate the moment gear Q produces if gear P produces a moment of 45 newton metres.

So pause the video, work out your solutions, and restart please.

Welcome back, and here's the solution to the first of those questions.

If you look at figure A, gear X is 10 teeth, gear Y is five teeth.

So gear Y will rotate two times for each turn of X.

Then you go onto the second one.

Gear X is 30 teeth and gear Y is 15.

So gear Y will rotate two times for each turn of X, again.

And finally, gear X is five teeth and gear Y is 15 type teeth.

So gear Y will rotate 1/3 of a revolution for each turn of X.

Well done if you've got those three.

And here's the final answers.

We calculate the force of the teeth from gear P, and that force is 180 newtons.

And then we use that to calculate the moment on the larger gear, and that gives 72 newton metres.

Well done if you've got that one.

And now, we've reached the end of the lesson.

So here's a quick summary.

A moment is the turning effect of a force.

And if an object is in equilibrium, there's no resultant force or resultant moment acting on it.

We can calculate a moment by moment equals force times distance normal to the direction of the force.

We've gotta take that into consideration.

And you can see my set of three diagrams showing which distances you should use for each situation.

Levers can act as force multipliers or distance multipliers.

And gears are used in machines, and they transfer forces from one place to another, and moments produced depend on the radius of the gears.

The moment is larger for a gear with a larger radius.

Well done for each in the end of the lesson, and I'll see you in the next one.