Forces & Newton’s Laws
What Is a Force?
A force is a push or a pull that acts on an object. Forces are measured in newtons (N). Every force arises because two objects are interacting — either by touching or at a distance.
Contact forces act when objects are physically in contact. Examples include friction, normal contact force, tension, and air resistance. Non-contact forces act at a distance through fields — gravitational force, electrostatic force, and magnetic force are all non-contact forces.
Forces always come in pairs. When two objects interact, each exerts a force on the other. These interaction pairs can be represented as vectors.
Scalars and Vectors
A scalar quantity has magnitude only. A vector quantity has both magnitude and direction. Force is a vector — it has a size and acts in a particular direction. Mass is a scalar — it has only size.
Key vector quantities include displacement, velocity, acceleration, force, and momentum. Key scalar quantities include distance, speed, mass, energy, and temperature.
A free body diagram shows all the forces acting on a single object. Each force is drawn as an arrow starting from the object. The length of the arrow represents the size of the force, and the direction of the arrow shows which way the force acts.
When the arrows are equal and opposite, the forces are balanced and the resultant force is zero. When they are unequal, there is a net (resultant) force and the object will accelerate.
Newton's First Law
Newton's first law states that if the resultant force acting on an object is zero, the object will remain stationary or continue to move at a constant velocity in a straight line. If the resultant force is not zero, the object will accelerate — its speed or direction (or both) will change.
An object moving at constant velocity has a resultant force of zero. It does not need a force to keep it moving — only to change its motion.
Newton's Second Law
Newton's second law tells us that the acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass. The equation is:
$$F = m \times a$$
where \(F\) is the resultant force in newtons (N), \(m\) is the mass in kilograms (kg), and \(a\) is the acceleration in metres per second squared (m/s²).
Weight is the force of gravity acting on an object. It is a vector quantity measured in newtons using a newton meter (spring balance). The equation is:
$$W = m \times g$$
where \(W\) is weight in newtons (N), \(m\) is mass in kilograms (kg), and \(g\) is the gravitational field strength in N/kg. On Earth, \(g = 10\) N/kg.
Mass is a scalar — it stays the same everywhere. Weight is a vector — it changes depending on the gravitational field strength.
Newton's Third Law
Newton's third law states that whenever two objects interact, they exert equal and opposite forces on each other. These forces act on different objects, are the same type of force, and are equal in magnitude but opposite in direction.
For example, when you push against a wall, the wall pushes back on you with an equal force. When Earth pulls you downward with gravity, you pull Earth upward with the same gravitational force.
Newton's third law pairs are always the same type of force, act on two different objects, are equal in size, and act in opposite directions.
Inertial mass is a measure of how difficult it is to change the velocity of an object. It is defined as the ratio of force over acceleration:
$$m = \frac{F}{a}$$
An object with a large inertial mass requires a large force to produce even a small acceleration. This is why it is much harder to push a loaded trolley than an empty one.
Circular Motion
An object moving in a circle at constant speed is constantly changing direction, so its velocity is changing. This means the object is accelerating, even though its speed stays the same.
For an object to move in a circle, there must be a resultant force acting towards the centre of the circle. This force is called the centripetal force. Without this force, the object would move in a straight line (Newton's first law). The centripetal force could be provided by tension, gravity, friction, or another force depending on the situation.
Exam Tip: When asked about Newton's laws, always identify the forces involved and state whether the resultant force is zero or not. For F = ma calculations, remember that F is the resultant force, not just any single force. Show your working clearly and include units in every step.
Forces are vector quantities that arise from interactions between objects. Newton's three laws explain how forces affect motion: the first law links zero resultant force to constant velocity, the second law quantifies the relationship \(F = ma\), and the third law states that forces always come in equal and opposite pairs. Understanding free body diagrams and the difference between mass and weight is essential for tackling force calculations in the exam.