Moments and beams in equilibrium
A moment is the turning effect of a force. For a beam that is not moving, the forces balance and so do the moments, which gives two equations to find unknown supports or positions.
Part 1 of 3: Learn it
In short
- The turning effect of a force is the force times its perpendicular distance from the pivot, measured in N m.
- In equilibrium: resultant force = 0 and clockwise moments = anticlockwise moments about any point.
- When a beam is about to tilt about one support, the reaction at the other support is zero.
Where this is in your specification
Spec points: DfE S1 (AQA 7357 S1, Edexcel 9MA0 Mechanics topic 9, OCR A H240 3.04)
| Board | Topic: Moments |
|---|---|
| DfE content | S1 |
| AQA 7357 | S1 |
| Edexcel 9MA0 | Mechanics topic 9 |
| OCR H240 | 3.04 |
The moment of a force
Multiply the force by the perpendicular distance from the point to the line of action of the force. State the direction: clockwise or anticlockwise. A force whose line passes through the point has no moment about it.
Equilibrium
- Resolve vertically: total upward force = total downward force.
- Take moments about a point: the clockwise total matches the anticlockwise total.
- Choose the point where an unknown force acts, so that force drops out of the equation.
Modelling beams
A uniform beam has its weight acting at its midpoint. A non-uniform beam has its centre of mass somewhere else, which may be the unknown. A rod or light beam has no weight. On the point of tilting about a support, the beam has just lost contact with the other support, so that reaction is zero.
Find the moment of a 25 N force acting 0.4 m from a pivot.
Show the answer
25 × 0.4 = 10 N m.
Part 2 of 3: See it worked
Worked examples
Example 1
A uniform plank AB is 4 m long and weighs 60 N. It rests on supports at A and at C, 3 m from A. Find the reactions.
- Weight acts at the midpoint, 2 m from A
- Moments about A: R_C × 3 = 60 × 2, so R_C = 40 N
- Vertically: R_A + 40 = 60, so R_A = 20 N
Answer: 20 N at A and 40 N at C.
Example 2
On a seesaw pivoted at its centre, a 300 N child sits 1.5 m to the left. Where must a 450 N child sit to balance it?
- Anticlockwise moment: 300 × 1.5 = 450 N m
- Clockwise moment: 450 × d
- 450d = 450
Answer: 1 m to the right of the pivot.
Common mistakes
- Using a distance that is not perpendicular to the force.
- Forgetting the beam's own weight.
- Taking moments about a point but still including the force acting there.
- Assuming both reactions are non-zero when the beam is on the point of tilting.
Where does the weight of a uniform rod act?
Show the answer
At its midpoint.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
Find the moment of a 25 N force acting 0.4 m from a pivot.
25 × 0.4 = 10 N m.
Where does the weight of a uniform rod act?
At its midpoint.
What does "light" mean for a rod in a mechanics question?
It has negligible mass, so its weight is ignored.
Jobs that use this
- Structural engineer (opens a new tab)
- Civil engineer (opens a new tab)
- Mechanical engineer (opens a new tab)
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
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