Torque
Torque is the rotational equivalent of force — it is the tendency of a force to cause rotation about a pivot or axis. Mathematically, it is the cross product of the position vector (from the axis to the point of force application) and the force vector. Torque is essential in engineering design of engines, gears, wrenches, and any rotating machinery.
Key Formula
τ = r × F = r × F × sin(θ)
LaTeX: \tau = r \times F = r F \sin\theta
| Symbol | Meaning | Unit |
|---|---|---|
| τ | Torque | Newton-metre (N·m) |
| r | Perpendicular distance from axis to line of action of force | Metre (m) |
| F | Applied force | Newton (N) |
| θ | Angle between r and F vectors | Degree or Radian |
Worked Example
Problem
A mechanic applies a force of 80 N at the end of a 0.4 m wrench handle perpendicular to the handle. Calculate the torque produced on the bolt.
Solution
Step 1: Identify values. r = 0.4 m, F = 80 N, θ = 90° so sin(90°) = 1 Step 2: Apply torque formula. τ = r × F × sin(θ) τ = 0.4 × 80 × 1 τ = 32 N·m
Answer
τ = 32 N·m
Typical Torque Values in Engineering and Everyday Life
| Application | Torque (N·m) | Notes |
|---|---|---|
| Bicycle pedal | 20–60 | Cyclist pedaling force |
| Car wheel lug nut | 100–150 | Manufacturer specified tightening torque |
| Car engine (petrol) | 150–400 | At peak RPM |
| Electric vehicle motor | 300–700 | Instant torque from standstill |
| Jet engine turbine | 100,000+ | Large commercial aircraft |
| Human wrist (twisting) | 2–5 | Maximum human wrist torque |
Interactive Tools
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Related Terms
Angular Velocity
Angular velocity is the rate of change of angular displacement of a rotating object with respect to time. It is a vector quantity whose direction is given by the right-hand rule along the axis of rotation. Angular velocity is the rotational analogue of linear velocity and is central to the analysis of rotating machinery, celestial bodies, and rigid body dynamics.
Moment of Inertia
Moment of inertia is the rotational analogue of mass — it measures an object's resistance to changes in its rotational motion about a given axis. It depends on both the total mass of the object and how that mass is distributed relative to the rotation axis; mass farther from the axis contributes more. Moment of inertia is fundamental in the design of flywheels, spinning tops, gyroscopes, and all rotating mechanical systems.
Angular Acceleration
Angular acceleration is the rate of change of angular velocity with respect to time. Like its linear counterpart, it is a vector quantity and represents how quickly a rotating object is speeding up or slowing down its rotation. Angular acceleration is produced by a net torque and is related to it by the rotational analogue of Newton's second law.
From Latin "torquere" meaning "to twist". The symbol τ is the Greek letter tau. The concept was developed through the work of Archimedes on levers and later formalized in the 19th century.