A wheel and axle has a wheel with a radius of 12 inches and an axle with a radius of 3 inches. If a force of 25 lbs is applied to the wheel, what force is exerted at the axle?

Wheel and axle is a simple machine where two cylinders of different radii are fixed together and rotate together. Mechanical advantage = radius of wheel / radius of axle = 12/3 = 4. Force at axle = 25 × 4 = 100 lbs. The wheel (larger radius) gets the input force; the axle (smaller radius) outputs the higher force. Trade-off: the axle moves a shorter distance — if the wheel rotates once and covers 2π(12) ≈ 75 inches at its edge, the axle rotates once and covers 2π(3) ≈ 19 inches. The same work (Force × Distance) is done by both. Wheel and axle applications: (1) STEERING WHEEL — large wheel turns steering column (axle) — force multiplier; (2) SCREWDRIVER — handle is the wheel, shaft is the axle — force multiplier for turning screws; (3) DOORKNOB — knob is wheel, latch mechanism is axle; (4) PENCIL SHARPENER — handle is wheel; (5) WINDLASS — well winch, anchor windlass; (6) FAUCET HANDLE — handle is wheel, valve stem is axle. Reverse application (speed multiplier instead of force multiplier): bicycle wheel — pedals/crank apply force at small radius (the axle), wheel rim (large radius) moves faster but with less force per unit of pedal force. Gears connecting wheels and axles transmit power efficiently in machines. The lever family (lever, wheel/axle, pulley) all share the principle of trading force for distance through rotational geometry.