Newton's laws of motion

First law (law of inertia)

An object at rest remains at rest, and an object in motion remains moving at the same speed in the same direction, unless acted upon by an unbalanced external force.

Newton's first law means that the following statements are equivalent (they are either all true or all false)

• The net force \(\vec{F}_{\text{net}}\) acting on an object is zero.
• The velocity \(\vec{v}\) of the object is constant.
• The change in the object's velocity \(\Delta\vec{v}\) is zero.
• The acceleration \(\vec{a}\) of the object is zero.

The term inertia means that physical objects lack the intrinsic ability to change their velocity. They must be affected by an external force for their velocity to change.

Second law (law of acceleration; law of momentum)

The acceleration of an object is directly proportional to the magnitude of the net force acting on it, and inversely proportional to the object's mass.

Using appropriate units of measurements, the second law is often written mathematically as

\[\vec{F}_{\text{net}}=m\vec{a}\]

In this form, force is measured in Newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). This also means that one Newton is equivalent to one kg·m/s².

For convenience, the arrows above vector quantities are frequently dropped (while maintaining the understanding that we are dealing with vectors). Newton's second law has a very important implication: the net force on an object and its acceleration always have the same direction.

Third law (law of action and reaction)

Every action has an equal and opposite reaction.

The third law means that no physical body can affect another with a force without getting itself equally affected in the opposite direction. In other words, forces always happen in pairs of equal magnitude and opposite direction. If object \(A\) affects object \(B\) with a force \(\vec{F}_{AB}\), then object \(B\) also affects object \(A\) with a force \(\vec{F}_{BA}\) acting in the opposite direction.

\[\vec{F}_{AB}=-\vec{F}_{BA}\]

The third law does not speak of the net force, while the first two are about the net force. The two forces \(\vec{F}_{AB}\) and \(\vec{F}_{BA}\) mentioned in the third law are never added to each other when calculating the net force, because they affect different objects.