Newton's First Law of Motion:

Every body perseveres in its state of being at rest or of moving uniformly straight forward, except in so far as it is compelled to change its state by forces impressed.

(Translated from the original Latin by I.E. Cohen and A. Whitman.)

In trying to understand the significance of this law, at least two questions need to be asked.

1. Is this law not just a special case of Newton's second law of motion:

The sum of all forces ₁, ₂, ... acting on a particle is equal to the product of the particle's mass m and the particle's acceleration ,

₁ + ₁ + ... = m ?

The second law implies that the acceleration of a particle is zero if no forces are acting on the particle; and for a particle's acceleration to be zero, the particle must either be at rest or moving with contstant speed in a straight line. Thus, Newton's second law does reduce to his first law when there are no forces acting on the particle.

2. What does it mean to say that a body is "at rest"? Does being at rest not depend on the frame of reference relative to which the body's motion is measured? E.g., a passenger in an accelerating car is at rest relative to the car, but he is in accelerated motion relative to the ground over which the car travels. Does Newton's first law hold equally well in the car frame of reference and in the ground frame of reference?

The answer is that Newton's first law holds in the ground frame of reference, but not in the car frame of reference. The passenger in the accelerating car experiences a force pushing him forward even though he is "at rest" relative to the car. Newton's first law does not hold in the car frame of reference because there is a force acting on the passenger and yet the passenger remains at rest relative to this frame.

This example illustrates that there is a difference between different kinds of reference frames, called inertial and non-inertial frames. Newton's first law and Newton's second law are valid in inertial frames of reference, but they are not true in non-inertial frames of reference.

How does one define inertial frames of reference? The definition is based on Newton's first law.

An inertial frame of reference is a reference frame relative to which Newton's first law of motion is true.

To test whether a reference frame is inertial, take an object that has no forces acting on it and make sure that the object is at rest relative to this frame at one moment. If the object remains at rest relative to this frame, the frame is inertial. In contrast, if an object stays at rest relative to some reference frame while there is a net force acting on the object, then this reference frame is non-inertial.

Through the definition of inertial frames, Newton's first law of motion acquires a new significance. When Newton's first law is taken to define inertial frames, it does not play the role of a special case of Newton's second law, but defines the circumstances under which Newton's second law applies. Newton's second law is not true in non-inertial frames. It is true only in inertial frames.

Newton's first law is also called the "Law of Inertia". For more information on this topic, go to the link under Related Items.