S: Moments — AQA A-Level Mathematics
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S: Moments explained
A moment measures the turning effect of a force about a point.
Read the full explanation
For a force F acting perpendicular to a rod at distance d from the pivot, the moment is F × d, measured in newton-metres (N m). In simple static contexts a rigid body is in equilibrium, so the total clockwise moment about any point equals the total anticlockwise moment. To solve a problem, choose a pivot to eliminate an unknown force, resolve perpendicular components where the force is not at right angles, and form an equation. For example, a uniform beam of weight 200 N resting on two supports: taking moments about one support gives the reaction at the other. Always state the pivot and check units and directions.
Your focus
- Calculate the moment of a force about a point using force × perpendicular distance.
- Form and solve a moments equation for a simply supported beam or rod in equilibrium.
- Interpret and solve simple static problems involving uniform and non-uniform rods, including tilting.
S: Moments exam tips
Marking Points
- State the pivot point and confirm the body is in equilibrium before forming an equation.
- Use moment = force × perpendicular distance from the pivot, converting lengths to metres and forces to newtons.
- For a force at an angle, use the perpendicular component F sin θ or the perpendicular distance, not the full force along the rod.
- Take moments about a point to eliminate an unknown reaction or tension, then solve the resulting linear equation.
- Include the weight of a uniform rod as acting at its midpoint, and model a non-uniform rod by placing its weight at the centre of mass.
- Check the answer by taking moments about a second point or by resolving vertically.
Examiner Tips
- 💡Draw a clear diagram, mark the pivot and label every force with its distance from the pivot.
- 💡Choose the pivot at a point where an unknown force acts so that its moment is zero and disappears from the equation.
- 💡Show the moment equation before solving, and give the final answer with correct units and a sensible direction.
- 💡If a rod is on the point of tilting, set the reaction at the lifting support to zero before taking moments.
Common Mistakes
- Using the full force when it acts at an angle to the rod: correct by using the perpendicular component F sin θ or the perpendicular distance.
- Forgetting the weight of the beam or assuming it acts at the end: correct by placing the weight at the midpoint for a uniform beam.
- Mixing units, such as centimetres with newtons: correct by converting all lengths to metres before calculating moments.
- Adding moments on the same side of the pivot instead of equating clockwise and anticlockwise totals: correct by labelling each moment's direction.