Torque from Force and Distance

Torque: τ = r × F = r·F·sin θ

Torque, also called the moment of force, tells you how strongly a force tends to spin something about a pivot: τ = r × F, with magnitude τ = r·F·sin θ, in N·m. Here r is the lever arm, the perpendicular distance from the pivot to the line of action, and θ is the angle between r and F, which means torque peaks at 90°. The rotational version of Newton's 2nd law is τ = I·α. Apply 50 N perpendicularly at 0.3 m and you get τ = 15 N·m, which is why a longer wrench makes the job easier. Combustion engines put out high torque at low RPM for pulling power, while power itself, equal to τ·ω, climbs as the RPM rises.

Applications

Levers, pliers and wrenches all do the same trick: they extend r to amplify torque. A torque wrench dials in a precise τ so you can seat bolts like wheel lug nuts or engine heads without over-tightening them. Car spec sheets quote peak torque (Nm) alongside peak power (kW), where torque drives how hard the car accelerates off the line and power sets the top speed. Doors put their hinges far from the handle, so even a light push builds up enough τ to swing them open.

FAQ

Why is a longer wrench easier? Look at τ = r·F. Double the r and you only need half the F to reach the same τ.

Torque vs power? Power equals τ·ω. At low RPM an engine with high torque pulls hard. Wind the same engine up to high RPM and it makes more power, but the torque per revolution drops.

Why does angle matter? Rotation comes only from the part of F that runs perpendicular to r. Pull straight along r, at θ = 0°, and you get τ = 0.