Forces
Concise revision notes aligned to the O Level syllabus.
Types of Forces
Forces are vector quantities — they have both magnitude and direction. The SI unit of force is the Newton (N), measured with a Newton meter (spring balance).
| Type | Examples |
|---|---|
| Contact forces | Friction, normal reaction, tension, air resistance |
| Non-contact forces | Gravity, magnetic force, electrostatic force |
A contact force requires physical touching between objects. A non-contact force acts at a distance — gravity, magnetism, and electrostatic attraction all fall into this category.
Weight and Mass
Mass is the amount of matter in an object (kg). It does not change with location.
Weight is the gravitational force acting on that mass (N). It depends on the local gravitational field strength g.
W = mg
| Location | g (N/kg) |
|---|---|
| Earth surface | ≈ 10 |
| Moon surface | ≈ 1.6 |
| Deep space | ≈ 0 |
Mass is constant everywhere; weight varies with g. On the Moon, your mass is unchanged but your weight is about one-sixth of your Earth weight.
Newton's First Law — Inertia
An object will remain at rest or continue moving with constant velocity unless acted on by a resultant (net) force.
Inertia is the tendency of an object to resist changes in its state of motion. Greater mass → greater inertia.
- Balanced forces (resultant = 0) → no change in motion
- Unbalanced forces (resultant ≠ 0) → acceleration
A car travelling at constant speed on a straight road has a resultant force of zero — the driving force exactly equals the resistive forces (friction + air resistance).
Newton's Second Law — F = ma
The resultant force on an object equals its mass multiplied by its acceleration.
F = ma
| Quantity | Symbol | Unit |
|---|---|---|
| Resultant force | F | Newton (N) |
| Mass | m | kilogram (kg) |
| Acceleration | a | m/s² |
- Double the force → double the acceleration
- Double the mass (same force) → half the acceleration
F = ma only applies to the resultant force, not any single force in isolation. Always find the net force first.
Newton's Third Law — Action and Reaction
For every action force there is an equal and opposite reaction force, acting on a different object.
- A person pushes a wall with 30 N → the wall pushes the person back with 30 N
- A rocket expels gas downward → the gas pushes the rocket upward
Key point: Newton's Third Law pairs always act on two different objects, so they can never cancel each other out.
Resultant Forces
The resultant force is the single force that has the same effect as all individual forces combined.
- Forces in the same direction: add them
- Forces in opposite directions: subtract smaller from larger; direction follows the larger force
- Resultant = 0 → object is in equilibrium (stationary or constant velocity)
Friction
Friction is a contact force that opposes relative motion between surfaces. It arises from microscopic roughness at contact surfaces.
- Always acts opposite to the direction of motion
- Can be useful (brakes, gripping) or wasteful (engine wear)
- Reduced by lubrication, smooth surfaces, ball bearings
Terminal velocity occurs when the resistive force (friction + air resistance) equals the driving force, giving zero resultant force and constant speed.
Friction opposes motion — it never acts in the direction of motion. This is the most commonly confused sign convention in forces problems.
Moments and Turning Effects
The moment of a force is its turning effect about a pivot.
Moment = Force × perpendicular distance from pivot
Unit: Newton-metre (N·m)
Principle of Moments (for equilibrium):
Sum of clockwise moments = Sum of anticlockwise moments
Centre of gravity is the single point through which the entire weight of an object appears to act. For a uniform object it is at the geometric centre.
The distance in the moment formula must be the perpendicular distance from the line of action of the force to the pivot — not the straight-line distance along a tilted lever.
Pressure
P = F / A
| Quantity | Symbol | Unit |
|---|---|---|
| Pressure | P | Pascal (Pa) = N/m² |
| Force | F | Newton (N) |
| Area | A | m² |
Smaller area → greater pressure for the same force (knife blade, stiletto heel, drawing pin).
Pressure in a liquid at depth h:
P = ρgh
where ρ is the fluid density (kg/m³), g = 10 N/kg, h = depth (m).
- Pressure increases with depth
- Pressure acts equally in all directions at a given depth
- Hydraulic systems use Pascal's principle: pressure applied to an enclosed liquid is transmitted equally throughout
Pressure in a fluid depends only on depth, density, and g — not on the shape of the container. This is why pressure at the bottom of a wide lake equals pressure at the same depth in a narrow pipe.
Upthrust and Archimedes' Principle
Upthrust is the upward force exerted by a fluid on any object submerged (fully or partly) in it.
Archimedes' Principle: The upthrust on an object equals the weight of fluid displaced by the object.
Upthrust = weight of displaced fluid
- Object floats when upthrust = weight (average density ≤ fluid density)
- Object sinks when weight > upthrust (average density > fluid density)
A steel ship floats because its hollow shape gives it an average density less than water, displacing enough water for upthrust to equal its weight.
Equilibrium and Stability
An object is in equilibrium when:
- Resultant force = 0 (no translational acceleration)
- Resultant moment = 0 (no rotational acceleration)
Stability depends on:
- Height of centre of gravity — lower is more stable
- Area of base — wider is more stable
An object topples when the line of action of its weight falls outside its base. Low, wide objects (racing cars, double-decker buses full on the lower deck) are harder to topple.
Free Fall and Terminal Velocity
In free fall (no air resistance), all objects accelerate at g = 10 m/s² regardless of mass.
Skydiver sequence:
- Jump → weight > air resistance → accelerates downward
- Speed increases → air resistance increases
- Air resistance = weight → terminal velocity (constant speed, ~55 m/s)
- Parachute opens → air resistance suddenly > weight → decelerates
- New, lower terminal velocity reached (~5–8 m/s)
At terminal velocity the resultant force is zero, but the object is still moving — do not confuse zero resultant force with zero velocity.
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