OCR Specification focus:
‘State Newton’s three laws of motion and apply them to varied systems and interactions.’
Newton’s three laws of motion provide the foundation for classical mechanics, explaining how forces affect motion, equilibrium, and interactions between bodies across all physical systems.
Newton’s First Law of Motion – The Law of Inertia
Newton’s First Law describes how an object behaves when no net force acts upon it. It addresses the concept of equilibrium and forms the basis for understanding motion and rest.
Newton’s First Law of Motion: An object will remain at rest or continue to move at a constant velocity in a straight line unless acted upon by a resultant external force.
This law introduces the idea of inertia — the natural tendency of an object to resist any change in its state of motion.
Inertia: The resistance of any physical object to a change in its velocity or direction of motion.
Objects in equilibrium experience balanced forces. The sum of all forces acting on the object equals zero, resulting in no acceleration.
If stationary, it remains stationary.
If moving, it continues at a constant speed in a straight line.
Common applications include:
A spacecraft coasting through space with engines off continues moving at constant velocity.
A book resting on a table remains stationary due to equal and opposite normal and gravitational forces.
The first law defines an inertial frame of reference — one in which Newton’s laws hold true and no unbalanced external forces cause acceleration. In non-inertial (accelerating) frames, apparent or fictitious forces (such as centrifugal force) may appear.
Newton’s Second Law of Motion – Force and Acceleration
Newton’s Second Law establishes the quantitative link between force, mass, and acceleration, forming the central mathematical model of motion in mechanics.
Newton’s Second Law of Motion: The acceleration of an object is directly proportional to the net external force acting upon it and inversely proportional to its mass.
EQUATION
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Force (F) = mass (m) × acceleration (a)
F = rate of change of momentum (Δp/Δt)
F = ma when mass is constant
F = net external force, measured in newtons (N)
m = mass of the object, measured in kilograms (kg)
a = acceleration, measured in metres per second squared (m s⁻²)
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This law means that:
A larger force produces a greater acceleration for a given mass.
A larger mass requires more force to achieve the same acceleration.
The direction of the acceleration is the same as the direction of the net force.
The second law allows for predicting motion in dynamic systems. When forces act on an object, their vector sum (the resultant force) determines acceleration.
Parallelogram construction of two forces F₁ and F₂, with diagonal Fᵣ as the resultant. This makes explicit that forces are vectors and must be combined by components or head-to-tail methods. The diagram is limited to vector addition and contains no extra content beyond what is required here. Source
For multiple forces:
Resolve all forces into perpendicular components.
Calculate resultant force using vector addition.
Apply F = ma along each direction separately.
EQUATION
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Resultant Force (ΣF) = m × a
ΣF = vector sum of all external forces acting on the body
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Everyday applications illustrate this law:
A car accelerates when the driving force from the engine exceeds air resistance and friction.
An object falling under gravity accelerates because the weight acts unopposed (neglecting air resistance).
This law also connects force and momentum: when the mass is not constant, as in rocket propulsion, F = Δp/Δt provides a more general form describing the rate of change of momentum.
Newton’s Third Law of Motion – Action and Reaction
Newton’s Third Law explains how forces always exist in pairs and act on different bodies. It highlights the interaction between objects rather than the motion of a single body.
Newton’s Third Law of Motion: When two bodies interact, the force exerted by the first on the second is equal in magnitude and opposite in direction to the force exerted by the second on the first.
These forces are called an action–reaction pair.
Two skaters exert equal-magnitude, opposite-direction forces on one another, forming an interaction pair acting on different bodies. The diagram focuses solely on the third law and avoids extra details. This helps distinguish action–reaction pairs from balanced forces on a single object. Source
They:
Act on different bodies (never the same object).
Are equal in magnitude, opposite in direction, and of the same type (e.g. both contact forces or both gravitational).
Occur simultaneously, not sequentially.
Common examples include:
When a person pushes against a wall, the wall pushes back with an equal and opposite force.
When a rocket expels gas backwards, the gas exerts an equal and opposite force on the rocket, propelling it forward.
When a horse pulls a cart, the cart exerts an equal and opposite force on the horse, but motion results from the friction between the horse’s hooves and the ground.
To correctly identify action–reaction pairs:
Identify the two interacting objects.
Determine the type of force involved (contact, gravitational, tension, etc.).
Assign forces to different objects, ensuring equal magnitude and opposite direction.
It is important not to confuse these pairs with the balanced forces acting on a single object. Balanced forces lead to equilibrium (first law), whereas third-law pairs always involve two separate bodies.
Interconnection of Newton’s Laws
Although each law can be considered individually, they operate together to describe the full mechanics of motion and interaction:
The first law defines motion in the absence of a net force.
The second law quantifies the relationship between force and motion when forces are unbalanced.
The third law describes how forces arise from mutual interactions between bodies.
In analysing physical systems, physicists apply all three laws collectively to predict motion, forces, and equilibrium across situations ranging from particle mechanics to planetary orbits.
FAQ
Newton’s laws assume there are no unbalanced external forces acting on the frame itself. In accelerating or rotating frames, extra apparent forces (called fictitious or pseudo forces) appear, such as the centrifugal force in a turning car.
To ensure accuracy when applying Newton’s laws, physicists must work in a frame where:
Objects not acted on by external forces move in straight lines at constant speed.
The frame is either stationary or moving at constant velocity relative to the universe’s inertial frame.
Mass is a measure of the amount of matter in an object, expressed in kilograms. Inertia, on the other hand, is a property that describes resistance to changes in motion.
The greater an object’s mass, the greater its inertia.
A bowling ball resists acceleration more than a tennis ball because it has greater mass.
Therefore, mass quantifies inertia — they are proportional but not identical concepts.
Action–reaction pairs act on different bodies, not the same one. This means they cannot cancel each other.
For example, when a person pushes a wall:
The person exerts a force on the wall.
The wall exerts an equal and opposite force on the person.
Each body experiences one force of the pair, so motion depends on the resultant of forces acting on that body alone.
When mass is not constant, the more general form F = rate of change of momentum (Δp/Δt) must be used.
For a rocket:
Fuel burns and ejects exhaust gases backwards.
The rocket’s mass decreases while gases gain momentum in the opposite direction.
The force propelling the rocket forward equals the rate of change of momentum of the expelled gases.
This application cannot be simplified to F = ma because m changes continuously.
Before Newton, Aristotle believed a force was needed to maintain motion. Newton overturned this by showing that no force is required for constant velocity — only to change motion.
This shift introduced:
The concept of inertia (objects naturally continue their motion).
The distinction between force and motion.
A predictive, mathematical framework that underpins classical mechanics.
Newton’s laws established motion as governed by universal principles, not by the nature of objects themselves.
Practice Questions
Question 1 (2 marks)
State Newton’s First Law of Motion and explain what is meant by an inertial frame of reference.
Mark Scheme:
1 mark for correctly stating Newton’s First Law: An object remains at rest or moves with constant velocity unless acted upon by a resultant external force.
1 mark for defining an inertial frame of reference: A frame of reference in which no unbalanced forces act and Newton’s laws hold true (i.e. no acceleration when forces are balanced).
Question 2 (5 marks)
A student stands on a skateboard holding a heavy ball. The student throws the ball horizontally forward.
Using Newton’s three laws of motion, explain what happens to the motion of both the student and the ball after the throw.
Mark Scheme:
1 mark for applying Newton’s Third Law: The force exerted by the student on the ball is equal in magnitude and opposite in direction to the force exerted by the ball on the student.
1 mark for identifying that these forces act on different objects (the ball and the student).
1 mark for linking Newton’s Second Law: The ball accelerates forward due to the unbalanced force from the student’s hands; the student accelerates backwards due to the equal and opposite force from the ball.
1 mark for referring to conservation of momentum or equivalent reasoning that the total momentum of the system remains constant (no external forces act).
1 mark for correctly connecting Newton’s First Law: Both the student and the ball move at constant velocity after the throw since no further unbalanced forces act once contact ends.
