About this chapter
Moments closes Mechanics 1 with beams, planks and rods that must not turn. Surprisingly, it was the best-answered question on the January 2025 paper, with the part about being on the point of tilting as the one exception.
This chapter covers the moment of a force, resultant moments, equilibrium of a rod, uniform and non-uniform rods, tilting, ranges of positions, relationships between reactions, weights and masses, and modelling assumptions. The questions use planks, seesaws, cables and a diving board held down by a bolt.
The ten questions
- Q1 (6 marks): a uniform plank on two supports: both reactions, and how "uniform" was used.
- Q2 (6 marks): a beam hanging from two ropes with a load, where one tension is 1.5 times the other.
- Q3 (6 marks): a rod on two supports: the greatest mass at one end, then both reactions.
- Q4 (6 marks): a non-uniform rod on the point of tilting in two cases gives its weight and centre of mass.
- Q5 (6 marks): a light rod carrying three masses: the balance point, and how it moves when a mass is added.
- Q6 (10 marks): a beam held by two cables with a load, and the greatest load before a cable breaks.
- Q7 (10 marks): a man walking along a plank on two supports: the reactions and where he can stand.
- Q8 (11 marks): a non-uniform rod where one reaction is twice the other, then a mass at its end.
- Q9 (10 marks): a seesaw with two children: the unknown mass, the pivot force, and a new balance.
- Q10 (11 marks): a diving board held down by a bolt: the forces, and the heaviest diver it can take.
Key skills tested
Moment of a force. Moment = force × perpendicular distance from the point, measured in N m. State whether it is clockwise or anticlockwise.
Resultant moment. Add the moments about one point, taking one sense as positive. A zero resultant moment means no turning.
Equilibrium. Resolve vertically and take moments about one point, or take moments about two points. Choose a point where an unknown force acts.
Uniform or not. A uniform rod's weight acts at its midpoint. For a non-uniform rod, let the centre of mass be x m from one end.
Tilting. On the point of tilting about a support, the reaction at the other support, or the tension in the other rope, is zero. Take moments about the tilting point.
Ranges. For no tilting, both reactions must be zero or more, and each tilting case gives one end of the range of positions.
Relationships. For conditions such as one reaction being twice the other, write both forces in one unknown before taking moments.
Weights and masses. A mass of m kg has weight mg newtons. If a weight is already given in newtons, do not multiply by g again.
Modelling. A rod is rigid and stays straight; uniform means its weight acts at the middle; a particle's weight acts at a single point.
Worked example
Question 1 from this chapter. A uniform plank AB of length 4 m and mass 20 kg rests horizontally on supports at A and at C, where CB = 1 m. Find (a) the reaction at C and (b) the reaction at A. (c) State how you used the fact that the plank is uniform.
(a) Take moments about A. The weight 20g acts at the midpoint, 2 m from A, and C is 3 m from A. So 3 × R at C = 20g × 2, giving 40g/3 = 131 N.
(b) Resolving vertically, the two reactions add up to 20g, so the reaction at A is 20g/3 = 65.3 N.
(c) The weight acts at the midpoint of the plank, 2 m from A.
Seen on real papers
Every question in our booklets is original. These are the recent papers where each question type has appeared.
- January 2025, Q4: a beam held by two vertical cables with a load, then the point of tilting when a tension becomes zero, as in Q2 and Q6.
Where marks are lost
- On the point of tilting. In January 2025 a significant number did not understand what this meant, and kept using a tension or a load that should have changed.
- Distances from the wrong point. Students who took moments about a point other than the one the question hinted at often made errors in the distances.
- Reusing old forces. Tensions from one part of the question were carried into another where they no longer applied. A new diagram for each part prevents this.
- Treating a force as a mass. A very small number treated a force in newtons as a mass and multiplied by g.
Common questions
Which point should I take moments about?
One where an unknown force acts, so it has no moment and drops out of the equation.
What does "on the point of tilting" tell me?
That the reaction at the other support, or the tension in the other rope, has just become zero.
Does a moment need a perpendicular distance?
Yes. For vertical forces on a horizontal rod, that is simply the distance along the rod.
Where this chapter leads
- Mechanics 1 Chapter 7: Statics of a Particle: the resolving that pairs with moments in equilibrium problems.
- Mechanics 1 Chapter 4: Dynamics of a Particle Moving in a Straight Line: forces and weights in moving systems.