Newton's laws of motion and F = ma
Newton's First Law (inertia)
An object will remain at rest or continue to move at a constant velocity unless acted upon by a resultant (net) force.
- Resultant force = 0: constant velocity (or stationary). Forces are balanced.
- Resultant force ≠ 0: the object accelerates (changes speed or direction).
Inertia is the tendency of an object to resist changes to its motion. Mass is a measure of inertia — a larger mass needs a larger force to produce the same change in motion.
Newton's Second Law (F = ma)
The resultant force on an object equals the product of its mass and acceleration.
$$F = ma$$
Where:
- F = resultant force (N)
- m = mass (kg)
- a = acceleration (m/s²)
Rearrangements:
- a = F/m
- m = F/a
Example: A 1200 kg car experiences a resultant force of 3600 N. Calculate its acceleration. a = F/m = 3600 / 1200 = 3 m/s².
Key points:
- F is the resultant (net) force, not just one force.
- If multiple forces act, find the resultant first (add if same direction, subtract if opposite).
- Weight (W = mg) is a force caused by gravity. g ≈ 10 N/kg (or m/s²).
Newton's Third Law (action-reaction)
When object A exerts a force on object B, object B exerts an equal and opposite force on object A.
Key features of Newton's 3rd law pairs:
- Equal in magnitude
- Opposite in direction
- Same type of force (e.g. both gravitational, both contact)
- Act on DIFFERENT objects
Example: A person pushes a wall with 50 N → the wall pushes the person back with 50 N in the opposite direction.
Common misconception: "If forces are equal and opposite, why does anything accelerate?" The forces act on DIFFERENT objects — they do not cancel out for the same object.
Free-body diagrams
A free-body diagram shows all the forces acting ON a single object (not forces the object exerts on others). Forces are represented as arrows from the centre of the object.
Example forces on a car:
- Weight (W, downward)
- Normal reaction force from road (R, upward)
- Driving force (F_drive, forward)
- Air resistance / friction (F_drag, backward)
Resultant force = F_drive − F_drag (horizontal).
If F_drive > F_drag → net forward force → accelerates. If F_drive = F_drag → zero net force → constant velocity.
Terminal velocity
Objects falling through a fluid (air, water) eventually reach terminal velocity when the drag force equals the weight.
- Initially, weight > drag → net downward force → accelerates.
- As speed increases, drag increases.
- Eventually drag = weight → resultant force = 0 → constant velocity (terminal velocity).
⚠Common mistakes
- F is resultant force, not individual force — if a 5 N force right and 3 N force left, F = 2 N right.
- Newton's 3rd law pairs act on DIFFERENT objects — they cannot cancel each other.
- Weight ≠ mass: weight W = mg (newtons); mass m (kg) is constant.
- Terminal velocity = constant velocity, not maximum speed that increases — it is a fixed value where drag balances weight.
AI-generated · claude-opus-4-7 · v3-edexcel-combined-science