How do large and small gears on the same shaft demonstrate a wheel and axle?
The wheel and axle is a simple machine designed to amplify force. When large and small gears are attached to the same shaft, they demonstrate this principle by showing how a force applied to a larger radius can overcome a greater force at a smaller radius.12
In this configuration, the shaft acts as the axle, while the gears function as wheels of different diameters. The mechanical advantage of the system is determined by the ratio of the radii of the two gears. Specifically, a force applied at the radius of the large gear creates enough torque to turn the shaft and overcome a larger force acting at the radius of the small gear. This relationship is expressed as:12
- Mechanical Advantage =
Where R is the radius of the large gear and r is the radius of the small gear. This setup effectively demonstrates how the wheel and axle modifies input force to perform work, such as lifting weights.12