Torque
Rotational effect of a force about a pivot.
Formula
Variables
Example
Longer wrench, more torque
How it works
Torque tells you how strongly a force tends to turn an object around a pivot. It depends not just on the size of the force, but also on how far from the pivot it is applied and on the angle: only the perpendicular part of the force actually produces turning, which is why the factor sinθ appears. A force applied closer to the pivot, or more nearly along the line to the pivot, produces less rotation.
When to use it
Use this formula whenever you need to find the turning effect of a force on a door, lever, nut, seesaw, or any object that can rotate about a pivot. It is also useful in mechanics problems involving balance, moments, and rotational equilibrium.
Worked example, step by step
A gardener pushes on a gate with a force of 50 N at a point 0.80 m from the hinges. The force is applied at an angle of 60° to the gate. Use: τ = rFsinθ Substitute: τ = 0.80 × 50 × sin(60°) Calculate sin(60°) ≈ 0.866 τ = 0.80 × 50 × 0.866 τ = 34.64 N·m Final answer: the torque is about 34.6 N·m.
Common mistakes to avoid
- Using the full force even when the force is not perpendicular; only the perpendicular component counts.
- Measuring r from the point where the force is applied instead of from the pivot.
- Forgetting units for torque, which are newton-metres (N·m).
Did You Know?
A long wrench multiplies your torque, which is why a cheater bar loosens a stubborn bolt so easily.
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