I recently made a bit of a mess of teaching the topic of gears by trying to ‘wing it’ with insufficient preparation. To avoid my — and possibly others’ — future blushes, I thought I would compile a post summarising my interpretation of what students need to know about gears for AQA GCSE Physics.

I am going to include some handy gifs and a clean, un-annotated Google Jamboard (my favoured medium for lessons).

Any continuing errors, omissions or misconceptions are entirely my own fault.

## ‘A simple gear system can be used to transmit the rotational effect of a force’ [AQA 4.5.4]

A gear is a wheel with teeth that can transmit the rotational effect of a force.

For example, in the gear train shown above, the first gear (A) is turned by a motor (green dot shown below). The moment (rotational effect) is passed via the interlocking teeth to gear B and so on down the chain to gear E. It is also worth pointing out that gear A has a clockwise moment but gear B has an anticlockwise moment. The direction alternates as we move down the chain. It takes a gear train of five gears to transmit the clockwise moment from gear A to gear E.

Gears A-E are all equal in size with the same number of teeth and, consequently, the moment does not change in magnitude as it passes down the chain (although, as noted above, it does change direction from clockwise to anticlockwise).

## ‘Students should be able to explain how gears transmit the rotational effect of forces’ [AQA 4.5.4]

### Part 1: A reduction gear arrangement

The driving gear (coloured blue) is smaller and has 6 teeth compared with the large gear’s 18 teeth. This is called a *reduction gear* arrangement.

A reduction gear arrangement does two things:

- It slows down the speed of rotation. You may notice that the large gear turns only one for each three turns of the small gear.
- The larger gear exerts a larger moment than the smaller gear. This is because the distance from the centre to the edge is larger for the grey gear.

The blue gear A exerts a force *F _{A}* on gear B. By Newton’s Third Law, gear B exerts an equal but opposite force

*F*on gear A. Let’s take the magnitude of both forces to be

_{B}*F*.

The anticlockwise moment exerted by gear A is given by *m = F x d*. The clockwise moment exerted by gear B is given by *M=F x D*. Since *D > d* then *M > m*.

A reduction gear arrangement is typically used in devices like an electric screwdriver. The electric motor in the device produces only a small rotational moment *m* but a large moment *M* is needed to turn the screws. The reduction gear produces the large moment *M* required.

### Part 2: The overdrive arrangement

What happens when the driver gear is larger and has a greater number of teeth than the driven gear? This is called an overdrive arrangement.

The example we are going to look at is the arrangement of gears on a bicycle.

Here the driver gear (on the left) is linked via a chain to the smaller driven gear on the right. This means that the anticlockwise moment of the first gear is transmitted directly to the second gear as an *anticlockwise* moment. That is to say, the direction of the moment is not reversed as it is when the two gears are directly linked by interlocking teeth.

In the example shown, the big gear A turns only once for each four turns completed by the smaller gear B. Let’s assume that gear A exerts a force *F* on the chain so that the chain exerts an identical force *F* on gear B. Since *D > d,* this means that *M > m* so that the arrangement works as a *distance multiplier* rather than a *force multiplier*. This is, of course, excellent if we are riding at speed along a horizontal road. However, if we encounter an upward incline we may wish to — using the gear changing arrangement on the bike — swap the small gear B with one with a larger value of *d*. This would have the happy effect of increasing the magnitude of *m* so as to make it slightly easier to pedal uphill.

The annotate-able Jamboard is available here.

## Acknowledgements

I used Gear Generator, Gear Generator 2 and EZgif to produce the gear animations.