Let us now examine the interpretation of the law in a bit more detail as the statement may not be completely in agreement of what we see around.

A body at rest remains at rest

The part of the statement, which says that the body remains in stationary state, is a comprehensible argument, supported by our daily life experience. We actually experience that a body requires some external force to be moved around form its stationary state. As a matter of fact, this experience instills the notion that the state of rest is the natural state of matter. We, however, know that notion of rest is actually an experience or a perspective in specific reference. A body at rest in Earth's reference is in motion for other heavenly bodies.

Rest does not mean absence of force. The body, in question, may actually experience a system of force whose net force is zero. Consider a book lying on the study table. The book experiences two forces (i) its weight acting downwards and (ii) normal reaction of the table acting upwards. The two forces are equal and opposite and hence their resultant is zero.

Figure 1: The book is acted upon by a pair of balanced forces.

Books lying on a table

In the nutshell, this part of first law of motion provides additional possibility of rest other than when rest may result from “no force” being applied to the body. This part of the law, therefore, characterizes two important aspects of rest as :

• Rest may arise from “no force” being applied on the body.
• Rest may arise from “zero net force” being applied on the body

Newton’s first law of motion can be interpreted to mean that objects do not change its state of motion on its own. This property of an object is known as “inertia” i.e. sluggishness or inactivity.

The property of the object of maintaining state of motion unless being forced externally is characterized by first law. For this reason, Newton’s first law is also referred as “law of inertia”. Incidentally, “inertia” is quantized by Newton’s second law of motion, which measures the “unwillingness” on the part of an object to change. Every object resists change in velocity.

A body moves with acceleration only when it is acted by external net force. The amount of acceleration i.e. rate of change in velocity for a given net force is different for different mass of the bodies.

From Newton's second law of motion (we shall read about this law in next module) :

F = ma

For a given force, F, we have :

⇒ a ∝ 1 m ⇒ a ∝ 1 m

In words, a smaller mass yields a greater acceleration and a greater mass yields a smaller acceleration. Thus, “mass” of a body is the measure of the inertia of the body in translational motion. Here, we have specified that mass is the measure of inertia in translational motion, because the inertia to rotational motion is measured by a corresponding rotational term called "moment of inertia".

The relation between Newton’s first law and inertial frame of reference is very close. The inertial frame of reference is actually defined in terms of Newton’s first law.

Definition 3: Inertial frame of reference

A frame of reference in which Newton’s laws of motion are valid is called inertial frame of reference.

An inertial frame of reference, where Newton’s first law is valid, moves with constant velocity without acceleration. A frame of reference moving with constant relative velocity with respect to an inertial frame of reference is also inertial frame of reference. The context of inertial frame of reference is important for Newton’s first law. Otherwise, we may encounter situations where a body may be found to be accelerated, even when net force acting on the body is zero. Consider the book lying on the floor of an accelerated lift moving upward.

Figure 2: The book is acted upon by a pair of balanced forces.

Books lying on the floor of an accelerated lift

To an observer in the lift, the books are under a pair of balanced forces : the weight of the books acting downward and an equal normal force acting upward. The net force on the book is zero. An observer on the ground, however, finds that book is accelerated up. To support this observation in Earth's inertial frame, the observations in the lift has to be incorrect.

This apparent paradox is resolved by restraining ourselves to apply Newton's first law in the inertial frame of reference only. The observer on the ground determines that the book is moving with upward acceleration. He concludes that the normal force is actually greater than the weight of the books such that

Figure 3: The book is acted upon by a net force.

Books lying on the floor of an accelerated lift

N - mg = ma

Aletnatively, we may use the technique of psuedo force and convert the accelerated frame into an inertial frame and then apply Newton's first law. We shall discuss this technique subsquently.

Further, we can always convert an accelerated non-inertial frame of reference to an equivalent inertial frame of reference, using the concept of “pseudo force”. This topic will be dealt in detail separately.

We, now, sum up the discussion so far as :