Torque and the Turning Effect of Force
Simple Explanation
Torque measures how effectively a force causes rotation about a pivot point. It depends on the size of the force, how far from the pivot it is applied, and the angle at which it is applied.
Why Do We Need It?
Torque is the rotational equivalent of force — just as force causes linear acceleration, torque causes angular (rotational) acceleration, and is fundamental to understanding anything that turns, spins, or rotates.
Formula
Torque (Turning Effect of Force)
τ = r F sinθ
Torque measures the turning effect of a force applied at some distance from a pivot — it depends on the force, the distance from the pivot, and the angle between them.
- τ
- — Torque, in newton-metres (N·m)
- r
- — Distance from the pivot (axis of rotation) to where the force is applied, in metres
- F
- — Magnitude of the applied force, in newtons
- θ
- — Angle between the force direction and the line from the pivot to the point of application
When to use it: Use to calculate the turning effect of a force about a pivot point — maximum torque occurs when the force is applied perpendicular to r (θ = 90°).
Worked Example
Calculating torque on a wrench
A 200 N force is applied perpendicular to a wrench, 0.25 m from the bolt. Find the torque.
Why Does This Work?
Torque depends on force AND on how far from the pivot (and at what angle) the force acts because the same force applied farther from a pivot, or more perpendicular to the lever arm, produces a greater rotational effect — this is the basic principle behind levers, wrenches, and spanners.
Real-Life Example
Using a longer wrench for a stuck bolt
Mechanics often use a longer wrench (or add a pipe extension) to loosen a very tight bolt.
Since τ = rF sinθ, increasing r (the effective lever arm length) lets the same applied force produce a larger torque — this is exactly why extending the wrench handle makes loosening a stuck bolt easier.
Practice
A 50 N force is applied perpendicular to a 0.6 m lever. Find the torque.
MediumCommon mistake
Forgetting the angle factor (sinθ) and just multiplying force by distance — torque is maximised only when the force is perpendicular to the lever arm (θ=90°); at other angles, only the perpendicular component of the force contributes.
Quick Review
- τ = rF sinθ measures the turning effect of a force about a pivot.
- Maximum torque occurs when force is perpendicular to the lever arm.
- A longer lever arm (r) means more torque for the same force.