Moments, levers and gears (physics only)

A pivot is a fixed point that an object can rotate about but cannot move away from. If a force acts along a line that passes directly through the pivot, it has no turning effect — the object doesn't rotate. If the force's line of action passes some distance from the pivot, the object rotates about the pivot in the direction of the force.

The distance d must be the perpendicular distance from the pivot to the line along which the force acts — if the force isn't applied at right angles to the object, you must use the perpendicular distance to its line of action, not the distance along the object itself. Example: pressing down on a bicycle pedal creates a moment about the pedal's pivot, turning the pedal arm.

Levers use a pivot to make a task easier: applying a force over a large distance from the pivot creates a large moment, which can move a load acting close to the pivot with much less force than would otherwise be needed.

Gears are circular, toothed wheels that mesh together to transfer a turning effect (moment) from one to another. Two meshed gears always turn in opposite directions to each other. If a gear supplying force turns a smaller gear (fewer teeth), the smaller gear turns faster but with less force. If it turns a larger gear (more teeth), the larger gear turns slower but with more force — because for the same force, a larger gear's teeth act further from its pivot, giving a bigger moment.