What determines the mechanical advantage in a wheel and axle system?

In a wheel and axle system, the mechanical advantage is determined by the ratio of the radius of the wheel to the radius of the axle. This relationship highlights how the different sizes of the wheel and axle work together to make lifting loads easier.

When a force is applied to the wheel, it is used to turn the axle. If the wheel has a larger radius, then more distance is covered with each rotation compared to the axle, which enables a smaller radius to provide a greater force in lifting. Essentially, the larger the radius of the wheel relative to that of the axle, the greater the mechanical advantage, making it easier to move or lift heavier loads.

This principle of leverage enables systems like bicycles or cranes to function effectively, where the user's input force on the wheel results in a larger output force at the axle, allowing for effective movement or lifting of heavy objects.