Levers and Gears

Levers and gears are simple machines that use the principle of moments to multiply force or change the direction of a force.

Levers

A lever is a rigid bar that rotates about a pivot (fulcrum). By increasing the distance from the pivot to the effort, a small effort force can produce a large load force.

$F_{\text{effort}} \times d_{\text{effort}} = F_{\text{load}} \times d_{\text{load}}$

If $d_{\text{effort}}$ is larger than $d_{\text{load}}$, then $F_{\text{effort}}$ is smaller than $F_{\text{load}}$. The lever provides a mechanical advantage.

Examples: crowbar, wheelbarrow, scissors, nutcracker, see-saw.

Classes of lever

• Class 1: pivot between effort and load (e.g. see-saw, scissors)
• Class 2: load between pivot and effort (e.g. wheelbarrow, nutcracker)
• Class 3: effort between pivot and load (e.g. tweezers, fishing rod). These multiply distance/speed at the expense of force.

Gears

Gears are interlocking toothed wheels. When one gear turns, the next gear turns in the opposite direction.

A small gear driving a large gear: the large gear turns more slowly but with greater force (torque). A large gear driving a small gear: the small gear turns faster but with less torque.

$\frac{\text{turns of gear A}}{\text{turns of gear B}} = \frac{\text{teeth on B}}{\text{teeth on A}}$

Common errors and how to correct them

• Forgetting that gears reverse the direction of rotation.
• Not using perpendicular distance from the pivot in lever calculations.

How to apply this in an exam

Identify the pivot, draw the forces, measure perpendicular distances and apply the principle of moments.