What is Torque?
Torque is the rotational equivalent of force — it measures how effectively a force causes an object to rotate around a pivot point. It's what makes a wrench turn a bolt or a door swing on its hinges.
Torque is the turning effect of a force around a pivot: τ = F·d·sinθ, where F is the applied force, d is the distance from the pivot, and θ is the angle between the force and the lever arm.
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Step-by-step worked examples
A wrench applies a 100 N force perpendicular to a 0.3 m bolt handle. Find the torque.
τ = F·d·sinθ θ = 90° so sinθ = 1 τ = 100 × 0.3 × 1 τ = 30 N·m
A 20 N force is applied to a door at 60° from the hinge line, 0.8 m from the hinge. Find the torque.
τ = F·d·sinθ τ = 20 × 0.8 × sin(60°) τ = 16 × 0.866 τ ≈ 13.86 N·m
A 150 N force is applied parallel to a 0.5 m lever arm (θ = 0°). Find the torque.
τ = F·d·sinθ θ = 0° so sinθ = 0 τ = 150 × 0.5 × 0 τ = 0 N·m
Flashcards
Quick quiz
Q1.What is the formula for torque?
Q2.At what angle between force and lever arm is torque maximum?
Q3.What is the SI unit of torque?
Q4.A force applied exactly along the lever arm (θ = 0°) produces…
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Common mistakes
Assuming τ = F·d always, ignoring the angle. — Correct: The full formula is τ = F·d·sinθ; the sinθ factor matters unless the force is exactly perpendicular.
Confusing torque's unit (N·m) with energy's unit (Joule), thinking they're the same quantity. — Correct: They share the same units dimensionally, but torque is a vector quantity related to rotation, not energy.
Using the force magnitude regardless of its direction relative to the lever arm. — Correct: Only the component of force perpendicular to the lever arm contributes to torque.
Measuring distance from the force's point of application to any reference, not the pivot. — Correct: d must be measured from the pivot (axis of rotation) to the point of application of the force.
FAQ
What is the formula for torque?
τ = F·d·sinθ, where F is force, d is the distance from the pivot, and θ is the angle between the force and lever arm.
How do you calculate torque?
Multiply the force by the lever arm distance and by sin of the angle between them: τ = F·d·sinθ.
What are examples of torque in everyday life?
Turning a wrench, opening a door, pedaling a bicycle, and tightening a bolt with a screwdriver all involve torque.
What is the difference between force and torque?
Force causes straight-line acceleration; torque causes rotational (angular) acceleration around a pivot.