Newton's first law or law of inertia

Newton's first law or law of inertia

Newton's first law is a fundamental law of dynamics, that is, of the movements of bodies. This law was developed by Isaac Newton and is also commonly called the law of inertia because inertia is the resistance to change (constant speed).

Newton's first law states that:

"Every body continues in a state of rest or uniform motion in a straight line unless it is compelled to change this state by forces imposed on it."

If an object has zero acceleration if it is in a state of rest or of uniform rectilinear motion. Therefore, this law can also be expressed as follows: "If no external force is exerted on an object, the acceleration of the object is zero." The force that an object exerts is proportional to the product of the mass and the acceleration.

Examples of Newton's First Law

A dynamometer

A common application is to weigh an object on a dynamometer. When placing an object on the dynamometer the object will experience two forces in opposite directions:

  • a net force that will push it down (force of gravity).

  • On the other hand, the dynamometer will exert a reaction force in the opposite direction by the principle of action reaction.

When the force exerted by the dynamometer equals the force caused by the weight of the object, the body will remain at rest. Therefore the law of inertia applies: if the sum of the forces acting on the object is zero, the acceleration is zero.

The rotation of the planets in the Solar System

The planets rotate around the Sun thanks to the force of gravity of the Sun. Without the presence of the Sun, the planets would describe a linear trajectory with a constant speed. However, the Sun exerts a centripetal force on the planets that causes a centripetal acceleration that constantly changes its trajectory causing them to rotate around it.

Newton's First Law Reference Systems

The first law of inertia cannot be applied in all reference frames.

Let us apply the law to a stone (object “A”) located in a street (reference frame 1) on which no force is applied.

The acceleration of the stone with respect to the reference frame 1 is zero and, therefore, the law of inertia is satisfied.

Now suppose that a car (reference frame 2) is accelerating relative to system 1. In this case, an observer in the car would see the stone accelerate without any force being applied to it. Therefore, the law of inertia cannot be applied to any reference frame if it is accelerated with respect to the first frame.

Newton's first law can only be applied to a special kind of frame of reference. This system is called an inertial reference frame. For a reference frame to be inertial it has to move with a constant relative velocity with respect to the first reference frame.

Publication Date: November 6, 2021
Last Revision: November 6, 2021