The Wheel and Axle
The wheel and axle is a simple machine consisting of a wheel attached to a smaller axle so that these two parts rotate together, allowing force to be transferred from one to the other.
The mechanical advantage heavily depends on which part you apply the force to.
- Multiplying Force: If you turn the large wheel to move the small axle (like a car steering wheel or a doorknob), you multiply your force.
- Multiplying Speed: If you turn the axle to spin the large wheel (like the drive axle of a car rotating the large tires, or a ceiling fan motor spinning large blades), you multiply speed and distance at the expense of force.
The Formula
Where:
IMA=
Ideal Mechanical Advantage=
Radius of the larger wheel=
Radius of the smaller axleExample Calculation
Consider a heavy wooden ship steering wheel with a radius of $50 , ext{cm}$ connected to a central steering column (axle) with a radius of $5 , ext{cm}$.
- Divide Wheel Radius by Axle Radius: $50 / 5 = 10$.
When the sailor applies force to the outer edge of the large steering wheel, their input force is multiplied by exactly $10$ when transferred to the smaller steering column, making it much easier to turn the heavy rudder against ocean currents.