In an ideal wheel-and-axle system, how is the IMA calculated?

In an ideal wheel-and-axle system, the Ideal Mechanical Advantage (IMA) is determined by the ratio of the radius of the wheel to the radius of the axle. This is because the wheel moves a greater distance compared to the axle, and this difference in radius translates to a mechanical advantage in the system. The larger the wheel relative to the axle, the more force is exerted to overcome a load, resulting in a greater IMA.

When a force is applied to the wheel, it creates a torque that is proportionate to the radius of the wheel. In contrast, the axle, being smaller in radius, requires less force to lift the same load as the wheel. Therefore, by dividing the radius of the wheel by the radius of the axle, we can quantitatively express how much more advantage we gain by using the larger radius of the wheel to apply force to the smaller radius axle, highlighting the fundamental principle of leverage in simple machines. This understanding is crucial for manipulating forces in practical applications involving wheels and axles.