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KS4 Moments, levers and gears

If you are working through the sections of the Forces chapter of the AQA KS4 Physics Specification in their order, then you will already already have worked through Forces and their interactions, Work done and Energy transfer and Forces and elasticity.

Now we need to turn our attention to Moments, levers and gears.

In our work on Forces and Motion we wrote a lot about how a Resultant Force can cause an object to accelerate, decelerate, start moving and stop moving. But all of these assumed that our object was moving, or going to move, in a straight line. A Resultant Force, however, can do one more thing concerning motion! It can make an object "turn" or "rotate".

This is pretty obvious. For example, you turn a tap to release some water; you turn a handle to open a door; you push a door to close it and it turns or rotates about its hinges; a car driver uses a force to turn or rotate a steering wheel.
There are loads of examples of how forces are used to produce such "Turning Effects".

In the world of Physics, when a force is used to make an object turn, we call it a Turning Effect or a Moment and believe it or not, all of the devices used to produce these turning effects, such as the tap top or the steering wheel or even the door with its hinges and its handle, are all very simple "machines"!
They are called "machines" because they do a job and they make it easier for the user to do the job.

OK, let's look at one simple "machine", to consider how it does its job and how it makes it easier for the user to do the job.
Below you can see diagram 1, a hand gripping a spanner and using it to turn a nut.

Motor mechanics in garages all over the world use spanners everyday to undo or to tighten nuts and bolts. Now here's the thing - without such spanners they would find it very difficult to do their job!

This is what the motor mechanic discovers when he or she first uses a spanner:
The "turning effect" produced at the pivot depends on TWO things:
1) The size of the Force.
Pretty obvious; so it helps to be a big, strong, tough guy!. Hm, not such a good discovery for a lot of mechanics.
2) The length of the spanner.
Or more precisely, the distance between the pivot and where the force is applied. This is a much more exciting discovery; it means that any nut can be undone by any person so long as he or she has a long enough spanner!

So now you should be able to see how the spanner (a simple machine) makes it easier to do the job.

Let's look at another simple machine; this time a machine known as a lever since it is often used to lever objects from the ground; it was probably first used by the ancient Egyptians when they were building pyramids. See diagram 2 below.

The lever "works" very much like the spanner; the same two factors affect the size of the Turning Effect produced:
1) The size of the force, limited by the strength of the person.
2) The distance between the pivot and where the force is applied, limited only by the length of the lever.

Its time to write an official equation for the Size of the Turning Effect!

Before we move on, notice the very long definition of d or distance in the Turning Effect or Moment equation above.

The line of action of the force is the continuation of the red force arrow, shown as a grey dashed line; the distance, d, is the perpendicular distance from this line to the pivot.

Even if you are presented with the situation shown in diagram 4, the distance you would use is d, the perpendicular distance from the line of action of the force to the pivot.

You would not use the distance d2 because it is NOT the perpendicular distance from the line of action of the force to the pivot.

An even more extreme case is shown in the diagram 4(a); the lever has dropped or turned anticlockwise so much that the distance d is now much less than the actual length of the green lever.

(Eventually if the green bar drops all the way down, then d will be virtually zero and the Turning Effect will become zero.)

Its time to have a go at a few example calculations.

Balancing Moments

Do you think that the object in diagram 5 will balance?

It will balance if the T.E produced by the force on one side of the pivot equals the T.E produced by the force on the other side of the pivot.

A better way of stating this is:

The object will balance if:
the total clockwise moment about the pivot equals the total anticlockwise moment about the same pivot.
This statement is known as "the principle of moments".

A "see-saw" is probably the best example of balancing moments.

So, do you think that the object in diagram 5 will balance?

I don't think it will because the clockwise moment, due to F2 x d2 is smaller than the anticlockwise moment, due to F1 x d1.
In other words, the anticlockwise moment is NOT equal to the clockwise moment, so the object will NOT balance. Do you agree? I hope so.

However, look at diagram 6.

This time we have values! So we can do some calculating.
Also, immediately we can see that the force on the right has become larger, increasing the likelihood that now the clockwise moment will be large enough to balance the anticlockwise moment. So, let's see.

A very common type of "balancing moments" question is one which asks you to find an unknown force on one side of a pivot. The point with these types of questions is that they must start by stating that the object is balanced, otherwise you can't solve the problem.

We should do one more example; this time, one where there is more than one force on one side of the pivot. This is where the word "total" in the Principle of Moments" is really relevant.

Gears - transmitting rotational effects

The heading at the very start of this section was "Moments, levers and gears", but we have not mentioned gears, yet.

We have seen how a simple lever, like a spanner, can cause a Turning Effect; this is a type of Rotational Effect, but levers can't really transmit a continuous rotational effect.

So, this is where Gears come in to our discussion.
A pair (or more) of gears can be used to transmit a continuous rotational effect, eg. 2 gears are used on a bike; one connected to the pedals, known as the chainring, which the rider rotates, and one connected to the rear wheel, known as a cog. A chain links the 2 gears so that when the rider rotates the chainring, the cog also rotates. And so long as the rider keeps applying a force, the gears transmit the rotational effect of that force.

Diagram 1 on the right (or below) shows two gears as used on a bike; the larger gear is the chainring, turned by the rider's force, which is transmitted to the rear cog which rotates the bike wheel. Quite simple.

A more direct example of how a pair of gears work is shown in Diagram 2. Here, when the smaller gear is turned by some force, it directly rotates the larger gear, transmitting the rotating effect. But notice that this time the direction of the transmitted rotation reverses! This would be useless on a bike!
However, if you add a 3rd gear, then the direction of rotation would "correct" itself, and this is what is done in the gearboxes of cars where many gears are used to transmit the rotational force of the car engine.