Levers

1. A lever is a rigid bar that turns about a pivot.
2. The effort is the force you apply to the lever, and the load is the force the lever acts against.
3. The effort produces a moment about the pivot, and the lever transmits this turning effect along the bar to the load.
4. The lever just balances the load, or is on the point of moving it, when the moment of the effort equals the moment of the load about the pivot.
   1. $effort\times distance\; of\; effort\; from\; pivot=load\times distance\; of\; load\; from\; pivot$
5. Everyday levers include a crowbar, a claw hammer pulling out a nail, a bottle opener, a wheelbarrow, scissors, nutcrackers and a screwdriver levering the lid off a tin of paint.
6. Your forearm is a lever too, with the elbow as the pivot and the biceps muscle supplying the effort.

Levers as force multipliers

1. When the effort acts further from the pivot than the load, a small effort can balance a large load, so the lever acts as a force multiplier.
2. The force is multiplied by the ratio of the two distances from the pivot.
   1. $\frac{load}{effort}=\frac{distance\; of\; effort\; from\; pivot}{distance\; of\; load\; from\; pivot}$
   2. A crowbar with the effort $1.2m$ from the pivot and the load $0.10m$ from it multiplies the force by $\frac{1.2}{0.10}=12$.
3. A lever does not supply extra energy, because the effort has to move through a larger distance than the load.
   1. To raise the load at the end of that crowbar by $1cm$, the end you push on must move down by $12cm$.
4. When the effort is closer to the pivot than the load, as in your forearm or a pair of tweezers, the effort must be larger than the load, but the load moves further and faster.

Gears

1. A gear is a wheel with teeth around its edge.
2. When two gears mesh, the teeth of the turning gear push on the teeth of the other gear, so a turning effect is passed from one axle to another.
3. The gear turned by a motor, a handle or your feet is the driving gear, and the gear it turns is the driven gear.
4. Two meshing gears always turn in opposite directions, so a driving gear turning clockwise makes the driven gear turn anticlockwise.
   1. Placing a third gear between them makes the driven gear turn in the same direction as the driving gear.
5. Where the teeth meet, the two gears push on each other with equal and opposite forces, so the force at the rim is the same size for both gears.

Gears as force multipliers

1. The moment on each gear is the force at its teeth multiplied by its radius, the distance from its axle to its teeth.
2. When a small driving gear turns a large driven gear, the same force acts at a larger radius, so the driven gear has a larger moment.
3. The moment is multiplied by the ratio of the radii, which is the same as the ratio of the numbers of teeth.
   1. $\frac{moment\; of\; driven\; gear}{moment\; of\; driving\; gear}=\frac{teeth\; on\; driven\; gear}{teeth\; on\; driving\; gear}$
4. The larger gear turns more slowly, so the gain in turning effect comes at the cost of speed of rotation.
   1. A driving gear with $12$ teeth turning a driven gear with $36$ teeth must make three full turns for every one turn of the driven gear.
5. When a large driving gear turns a small driven gear, the moment is reduced, but the driven gear turns faster.
6. A bicycle uses the same idea, because a large rear sprocket gives a bigger turning effect at the wheel for climbing hills, while a small rear sprocket turns the wheel faster on flat roads.
7. A car gearbox and a hand drill also use gears to switch between a large turning effect and a high speed of rotation.