Newton’s first law of motion

An object does not need a force to keep moving at a steady speed in a straight line. It needs a resultant force to change its motion.

Newton’s first law states that an object remains at rest or continues moving with constant velocity in a straight line unless a resultant external force acts on it. An external force is a force exerted on the object by something outside it. The resultant force is the combined effect of all the external forces acting on the object.

When the resultant force is zero, the object has no acceleration. Its velocity does not change: if it is stationary, it stays stationary; if it is moving, it continues at the same speed in the same direction. Zero resultant force does not necessarily mean that no forces act. Forces can act in opposite directions and balance each other.

A resultant force is needed to change an object’s speed or its direction of motion. For example, a sliding object may slow down because friction exerts a force on it, not because motion itself requires a force to continue.

The tendency of an object to resist a change in its motion is called inertia. An object at rest tends to remain at rest, while a moving object tends to maintain its velocity.

Newton’s second law of motion

A force can change an object’s velocity, causing it to accelerate. When several external forces act on an object, their combined effect is the resultant force or net force. Newton’s second law connects this resultant force to the object’s acceleration.

For an object whose mass is constant:

Here, $$\mathbf{F}_{\mathrm{net}}$$ is the resultant external force, measured in newtons ($$\mathrm{N}$$); $$m$$ is mass, measured in kilograms ($$\mathrm{kg}$$); and $$\mathbf{a}$$ is acceleration, measured in metres per second squared ($$\mathrm{m/s^2}$$).

The acceleration is in the direction of the resultant force. For the same mass, a greater resultant force produces a greater acceleration: doubling the force doubles the acceleration. For the same resultant force, a greater mass produces a smaller acceleration: doubling the mass halves the acceleration.

For example, a resultant force of $$12,\mathrm{N}$$ to the right acting on an object of mass $$3,\mathrm{kg}$$ produces an acceleration of $$4,\mathrm{m/s^2}$$ to the right. If the resultant force is zero, the acceleration is zero; the object can still be moving at constant velocity.

Newton’s third law of motion

When two objects interact, each exerts a force on the other. Newton’s third law states that these two forces act simultaneously and are equal in magnitude but opposite in direction.

For example, when you push on a wall, your hand exerts a force on the wall. At the same time, the wall exerts an equally large force in the opposite direction on your hand. These forces form an interaction pair.

The forces do not cancel as forces on a single object: one acts on the wall, while the other acts on your hand. To find the total force on either object, consider only the forces acting on that object.