Moments — Edexcel A-Level Mathematics
Test yourself on Moments with PEARSON EDEXCEL A-Level practice questions.
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Moments explained
A moment measures the turning effect of a force about a point.
Read the full explanation
For a force F acting at perpendicular distance d from a pivot, the moment is Fd. In simple static contexts, a rigid body is in equilibrium when the sum of clockwise moments about any point equals the sum of anticlockwise moments about that point, and the resultant force is zero. To solve problems, choose a convenient pivot to eliminate unknown forces, resolve forces into components perpendicular to the line from the pivot, and apply the principle of moments. Example: a uniform metre rule of weight 2 N is pivoted at the 30 cm mark. A 5 N weight at the 10 cm mark gives an anticlockwise moment of 5 × 0.20 = 1.0 N m about the pivot; the rule’s weight acts at the 50 cm mark, giving a clockwise moment of 2 × 0.20 = 0.4 N m. To balance, an additional clockwise moment of 0.6 N m is needed.
Your focus
- Define the moment of a force and calculate it using the perpendicular distance from a pivot.
- State and apply the principle of moments to solve simple static equilibrium problems.
- Select an appropriate pivot and use perpendicular distances or resolved components to find unknown forces or distances in static systems.
Moments exam tips
Marking Points
- Define the moment of a force about a point as the product of the force and the perpendicular distance from the point to the line of action of the force.
- State the principle of moments for a body in equilibrium: the sum of clockwise moments about any point equals the sum of anticlockwise moments about that point.
- Choose a suitable pivot to simplify calculations, often eliminating unknown reaction forces at that point.
- Use perpendicular distances correctly, including resolving a force into components perpendicular to a given line when the force is not perpendicular to the distance.
- Apply the principle of moments to simple static systems such as beams, rods, levers and balanced masses, including cases with multiple forces and unknown distances or forces.
Examiner Tips
- 💡Draw a large, clear diagram showing all forces, their lines of action and the distances from the chosen pivot.
- 💡Choose a pivot that eliminates as many unknown forces as possible, often a support or hinge.
- 💡Write the principle of moments as an equation before substituting numbers, and keep units consistent (for example, convert cm to m if using N m).
- 💡Check that the sum of clockwise moments equals the sum of anticlockwise moments and that the resultant force is also zero for full equilibrium.
Common Mistakes
- Using the distance along the beam rather than the perpendicular distance from the pivot to the line of action of the force. Correction: always use the perpendicular distance, or resolve the force into a component perpendicular to the beam.
- Forgetting to include the weight of the beam or rod itself. Correction: include the weight acting at the centre of mass, which for a uniform beam is at its midpoint.
- Taking moments about a point but ignoring the direction of each moment. Correction: clearly assign clockwise and anticlockwise directions and equate their sums for equilibrium.
- Assuming a force acting through the pivot has a moment. Correction: a force whose line of action passes through the pivot has zero moment about that pivot.