In simple terms
A friendly intro before the formal notes — no formulas yet.
The Rules of Motion
Newton's laws are the three fundamental rules that predict how an object's motion will change when forces act on it. They are the essential toolkit for solving almost every problem in mechanics.
Imagine pushing a shopping trolley. To get it moving (accelerate it), you need to push it (apply a resultant force). The heavier it is (more mass), the harder you need to push for the same acceleration. When you stop pushing, it eventually stops due to friction. If there were no friction, it would just keep going at a constant speed forever (First Law). As you push the trolley, the trolley pushes back on you with an equal force (Third Law).
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First law: An object maintains constant velocity (including being at rest) unless a resultant force acts on it. This is the principle of equilibrium.
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Second law: The resultant force on an object is the product of its mass and acceleration (F=ma). Acceleration is always in the same direction as the resultant force.
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Third law: For every action, there is an equal and opposite reaction. These two forces act on different bodies and are of the same type.
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Weight is the force of gravity on an object. Near the Earth's surface, it is calculated as W = mg and always acts vertically downwards.
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Key formulas
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Full topic notes
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Newton's First Law: The Law of Inertia
Newton's First Law describes an object's tendency to resist changes in its state of motion. If an object is at rest, it wants to stay at rest. If it's moving, it wants to keep moving at a steady speed in a straight line. This only changes if a 'resultant' or 'net' force is applied. In many exam questions, this law is used to establish equilibrium, where the vector sum of all forces acting on an object is zero.
Equilibrium means the resultant force is zero: .
An object in equilibrium is either stationary or moving at a constant velocity.
This law is often used to solve for unknown forces by resolving forces in perpendicular directions (e.g., horizontally and vertically) and setting the sum in each direction to zero.
Newton's Second Law: The Core Equation
This is the most powerful and frequently applied of the three laws. It provides the mathematical relationship between the cause of motion (force) and the resulting change in motion (acceleration). The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass.
F_{net} = ma
Here, is the resultant force in Newtons (N), is the mass of the object in kilograms (kg), and is the acceleration in metres per second squared (m s⁻²). Remember that force and acceleration are vectors; the acceleration always takes place in the same direction as the resultant force.
Newton's Third Law: Action-Reaction Pairs
This law states that forces always occur in pairs. If object A exerts a force on object B, then object B simultaneously exerts a force on object A that is equal in magnitude and opposite in direction. The most important and often misunderstood aspect of this law is that the two forces in a pair act on different objects. This is why they do not cancel each other out.
A common mistake is to identify two forces that are in equilibrium on a single object as an action-reaction pair. For example, for a book on a table, the book's weight and the table's normal reaction force are NOT a third-law pair. They are just two forces that happen to be equal and opposite, acting on the same object (the book). The true reaction to the book's weight is the gravitational force the book exerts on the Earth.
Worked examples
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A box of mass 5 kg rests on a rough horizontal floor. The coefficient of friction between the box and the floor is 0.4. A horizontal force of 30 N is applied to the box. Find the acceleration of the box. (Take m s⁻²).
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Draw a force diagram. Identify all forces: Weight (), Normal Reaction (), Applied Force (30 N), and Friction ().
Two particles, A of mass 3 kg and B of mass 2 kg, are connected by a light inextensible string. Particle A is pulled along a smooth horizontal surface by a horizontal force of 40 N. Find the acceleration of the system and the tension in the string.
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Consider the system as a whole. Treat both particles as a single object with combined mass kg. The only external horizontal force is 40 N (tension is an internal force).
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Glossary
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What is Newton's First Law of Motion?
An object will remain at rest or continue to move with constant velocity unless acted upon by a resultant external force. This is also known as the law of inertia.
Key takeaways
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Equilibrium means the resultant force is zero: .
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An object in equilibrium is either stationary or moving at a constant velocity.
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This law is often used to solve for unknown forces by resolving forces in perpendicular directions (e.g., horizontally and vertically) and setting the sum in each direction to zero.
Practice — then mark it
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Test Your Knowledge on Newton's Laws
Test Your Knowledge on Newton's Laws
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