The turning effect of a force about a pivot. Moment = force × perpendicular distance from the pivot to the line of action of the force.
Moment = F × dMoment in N·m · F = force (N) · d = perpendicular distance from pivot (m)
Worked example
A 40 N force is applied 0.6 m from a pivot. Find the moment.
Moment = 40 × 0.6 = 24 N·m
Key word: perpendicular
The distance must be the perpendicular distance from the pivot to the LINE OF ACTION of the force — not the distance along the object. If a force is applied at an angle, you must use the perpendicular component.
2. Principle of Moments
Principle of Moments
For an object in equilibrium, the sum of clockwise moments about any pivot equals the sum of anticlockwise moments about the same pivot.
Worked example
A uniform beam is balanced. A 30 N weight sits 2 m to the left of the pivot. A force F acts 1.5 m to the right. Find F.
Anticlockwise moment = 30 × 2 = 60 N·m
Clockwise moment = F × 1.5
60 = F × 1.5 → F = 60 ÷ 1.5 = 40 N
3. Centre of Gravity
Centre of gravity
The single point through which the entire weight of an object appears to act.
For a uniform object (e.g. a metre rule), the centre of gravity is at its geometric centre. For irregular objects, suspend from two different points in turn — the centre of gravity lies at the intersection of the two plumb lines.
Stability increases when the centre of gravity is lower and the base is wider. A racing car has a wide wheelbase and low centre of gravity — it is very stable. A double-decker bus is less stable at high speeds because its centre of gravity is higher.
4. Pressure
Pressure
Force per unit area acting perpendicular to a surface.
P = F ÷ AP = pressure (Pa or N/m²) · F = force (N) · A = area (m²)
Worked example
A box exerts a force of 600 N on a floor of area 0.5 m². Find the pressure.
P = 600 ÷ 0.5 = 1200 Pa
Same force, smaller area = higher pressure
This is why a knife cuts (small edge area → large pressure) and snowshoes work (large area → small pressure on snow).
5. Pressure in Fluids
P = ρghP = pressure (Pa) · ρ = fluid density (kg/m³) · g = 10 N/kg · h = depth (m)
Pressure in a fluid acts equally in all directions at a given depth.
Pressure increases with depth (more fluid above = more weight pressing down).
Pressure in fluids depends only on depth and density — NOT on the shape of the container or the total volume of fluid. Two containers of different shapes but the same fluid at the same depth have the same pressure at that depth.
Moment of a Force
Moment (Nm) = Force (N) x Perpendicular distance (m)
Distance must be PERPENDICULAR from the line of action of force to the pivot
Pressure in Fluids
P = ρgh
P in Pa, ρ = fluid density (kg/m3), g = 10 N/kg, h = depth below surface (m)
Must-Know for Exam
Moment = F x perpendicular distance to pivot. Distance must be perpendicular - not along the object.
Principle of moments (equilibrium): sum of CW moments = sum of ACW moments
Stable equilibrium: low centre of gravity + wide base. Unstable: high CofG + narrow base.
Pressure P = F/A. Sharp knife: small area = high pressure. Snowshoes: large area = low pressure.
Fluid pressure P = rho x g x h. Depends on depth, fluid density, and g only - NOT shape of container.
6. Common Exam Traps
Trap 1 — Perpendicular distance
Moment = F × perpendicular distance. If a 50 N force pulls at an angle, you cannot just use the length of the arm — you must find the perpendicular component of the distance (or the perpendicular component of the force).
Trap 2 — Units of pressure
1 Pa = 1 N/m². Do not confuse kPa and Pa. Atmospheric pressure ≈ 101 kPa = 101 000 Pa.
Key Terms — Flashcard Review
Tap each card to reveal the definition.
Moment
Turning effect of a force. Moment = Force x perpendicular distance from pivot. Unit: Nm.
Principle of moments
For equilibrium: sum of clockwise moments = sum of anticlockwise moments about any point.
Centre of gravity
Point where entire weight of object appears to act. Object balances at its centre of gravity.
Pressure
Force per unit area. P = F/A. Unit: pascal (Pa) = N/m2. Greater area = less pressure for same force.
Pressure in fluids
P = rho x g x h. Increases with depth. Acts equally in all directions at the same depth.
Hydraulic systems
Pressure transmitted equally through liquid. Small force on small piston = large force on large piston.
🎯 Practice Quiz — Test Yourself
8 O Level-style questions on this topic. Select an answer to see instant feedback.
Question 1 of 8
A 20 N force acts 3 m from a pivot. The moment is:
Explanation: Moment = Force × perpendicular distance = 20 × 3 = 60 N m.
Question 2 of 8
For rotational equilibrium, the principle of moments states:
Explanation: Principle of moments: sum of clockwise moments = sum of anticlockwise moments about any pivot point.
Question 3 of 8
Pressure at depth h in liquid of density ρ is:
Explanation: P = hρg where h = depth (m), ρ = density (kg/m³), g = 10 N/kg.
Question 4 of 8
A sharp knife cuts easier than a blunt one with the same force because:
Explanation: P = F/A. Smaller area → greater pressure for same force → easier cutting.
Question 5 of 8
10 N at 2 m left of pivot. Where must 5 N be placed to balance?
Explanation: 10 × 2 = 5 × d → d = 4 m to the right.
Question 6 of 8
A force of 20 N acts 0.5 m from a pivot. The moment is:
Explanation: Moment = Force x perpendicular distance = 20 x 0.5 = 10 Nm. Always check the distance is perpendicular to the force direction, not along the lever arm.
Question 7 of 8
At a depth of 4 m in water (density 1000 kg/m3, g = 10 N/kg), the pressure due to water is:
Explanation: P = rho x g x h = 1000 x 10 x 4 = 40 000 Pa. This does not include atmospheric pressure (unless asked for total pressure). Remember: pressure in fluids increases linearly with depth.
Question 8 of 8
In a hydraulic press, a force of 10 N is applied to a piston of area 0.01 m2. The pressure transmitted to a larger piston of area 0.1 m2 produces a force of:
Explanation: Pressure in = F/A = 10/0.01 = 1000 Pa. Same pressure on large piston: F = P x A = 1000 x 0.1 = 100 N. Hydraulic systems multiply force by the ratio of piston areas.