Apply the principle of moments to other situations, including those with more than one force each side of the pivot

What is a moment?

A moment (or torque) is the turning effect of a force about a pivot.

It is calculated as the product of the force and the perpendicular distance from the pivot:

\$\text{Moment} = F \times d\$

⚖️ Think of a seesaw: the farther you sit from the centre, the easier you can tip it, even if you sit lighter.

Principle of Moments (Balance of Torques)

For a body in rotational equilibrium (not rotating), the sum of clockwise moments equals the sum of anticlockwise moments:

\$\sum M{\text{clockwise}} = \sum M{\text{anticlockwise}}\$

🔧 If you push down on one side of a lever, you must push up on the other side with a force that balances the moments.

Example 1 – Single pair of forces

Two forces act on a rigid bar pivoted at point O:

• \$F1 = 30\,\text{N}\$ at a distance \$d1 = 0.4\,\text{m}\$ (clockwise)
• \$F2 = 20\,\text{N}\$ at a distance \$d2 = 0.6\,\text{m}\$ (anticlockwise)

Check equilibrium:

\$30 \times 0.4 \;=\; 12 \;\text{N·m}\$

\$20 \times 0.6 \;=\; 12 \;\text{N·m}\$

Since the moments are equal, the bar is in equilibrium. 🎯

Example 2 – Multiple forces on each side

Now add a third force on the clockwise side:

• \$F1 = 30\,\text{N}\$, \$d1 = 0.4\,\text{m}\$
• \$F3 = 10\,\text{N}\$, \$d3 = 0.3\,\text{m}\$
• \$F2 = 20\,\text{N}\$, \$d2 = 0.6\,\text{m}\$

Calculate total clockwise moment:

\$M_{\text{cw}} = 30 \times 0.4 + 10 \times 0.3 = 12 + 3 = 15 \;\text{N·m}\$

Anticlockwise moment remains 12 N·m. Since \$M{\text{cw}} > M{\text{acw}}\$, the bar will rotate clockwise. 🚀

To bring it back to equilibrium, you could adjust one of the distances or forces.

Real‑world analogy – The Scissors

When you open a pair of scissors, the handle is the pivot. The force you apply at the handle creates a moment that opens the blades. If you press harder (larger \$F\$) or move your hand further from the pivot (larger \$d\$), you get a larger moment, making it easier to cut.

🔧 Remember: Force × Distance = Moment. The same rule applies to levers, door hinges, and even your own body when you lift something.

Exam Tips

1. Identify the pivot. All distances are measured from this point.
2. Mark directions. Use arrows or colour coding (red = clockwise, blue = anticlockwise).
3. Check units. Moments are in N·m. If you use cm, convert to m.
4. Set up the equation. Write \$\sum M{\text{cw}} = \sum M{\text{acw}}\$ and solve for the unknown.
5. Use diagrams. A clear sketch often reveals the correct distances.
6. Time management. Practice setting up the equation quickly – the calculation is usually straightforward.

💡 Practice with different configurations: a seesaw, a door, a crane. The more you see the same pattern, the easier it becomes.

Quick Check – Mini Quiz

Three forces act on a lever pivoted at O:

• \$Fa = 25\,\text{N}\$, \$da = 0.5\,\text{m}\$ (clockwise)
• \$Fb = 15\,\text{N}\$, \$db = 0.7\,\text{m}\$ (anticlockwise)
• \$Fc = 10\,\text{N}\$, \$dc = 0.4\,\text{m}\$ (clockwise)

Will the lever rotate clockwise or anticlockwise? Write your answer in the form “Clockwise” or “Anticlockwise”.

🧠 Think through the steps before answering!