How a lever transmits a turning effect

1. A lever is a rigid bar or handle that turns about a pivot, and it carries the turning effect of a force from one place to another.
2. The force applied by the user is the input force, sometimes called the effort, and the force the lever applies to the load is the output force.
3. The input force acts at a distance from the pivot, so it produces a moment, and it is that moment which is passed along the rigid lever to the load.
4. Because a moment is force multiplied by perpendicular distance, applying the input force further from the pivot produces a larger moment for the same effort.
5. A lever therefore acts as a force multiplier whenever the input force acts further from the pivot than the load does, so a small input force produces a large output force.
6. The gain in force is paid for in distance, because the end you push moves much further than the load moves, so the lever redistributes force and movement rather than creating energy.
7. Common levers all work in the same way.
   1. A crowbar prising up a floorboard, with the pivot at the point resting on the floor.
   2. A spanner turning a nut, with the pivot at the centre of the nut.
   3. A bottle opener lifting a cap, with the pivot at the lip resting on the cap.
   4. A wheelbarrow, with the pivot at the wheel and the load between the wheel and the hands.
   5. A pair of scissors, which is two levers sharing a single pivot.
8. In every case it is the moment of the input force about the pivot that is transmitted, so naming the pivot is the first step in any explanation.

How gears transmit a turning effect

1. A gear is a toothed wheel, and gears are used in pairs whose teeth interlock so that neither can turn without turning the other.
2. The gear that is turned first is the driving gear, and the gear it turns is the driven gear.
3. The teeth of the driving gear push on the teeth of the driven gear, and that contact force acts at a distance from the centre of the driven gear, so it produces a moment on it.
4. Because the two sets of teeth push each other in opposite directions, two gears that mesh directly always rotate in opposite directions.
5. Adding a third gear between them, called an idler gear, reverses the direction a second time, so the first and last gears then turn the same way.
6. A small driving gear turning a large driven gear makes the large gear rotate more slowly but with a larger moment, because the force from the teeth acts at a greater distance from its centre.
7. A large driving gear turning a small driven gear makes the small gear rotate faster but with a smaller moment.
8. Low gear on a bicycle uses exactly this trade off to climb a hill, because a small chain wheel driving a large rear sprocket gives a big turning effect at the wheel at the cost of pedalling faster for less road speed.
9. Car gearboxes, hand drills and clock mechanisms all rely on the same exchange between the size of the moment and the rate of rotation.