8.1 Newton's first law of motion

The first law of motion talks about the motion of a body for a particular situation. There is either "no force" or "zero net force" acting on the body. The first condition of "no force" is not common in our immediate surrounding. All bodies are acted by gravity i.e. force of attraction due to Earth. On the other hand, the second condition of "zero net force" is common in our immediate surrounding, where most bodies are stationary in Earth's reference as net force is zero.

First law of motion

Unless acted upon by a net external force, a body, at rest, will remain at rest and a body, in motion, will remain in motion.

The state of motion of a given body, including the state of rest, is completely defined by its velocity. Stationary state is just one important case of constant velocity or uniform motion. If the object is stationary in a frame of reference, then

v = 0

We can restate the first law of motion more concisely in velocity term as :

First law of motion

If net external force on a body is zero, then its velocity remains constant.

Mathematically equivalent statements of the first law of motion are :

1: If ∑ F = 0, then v = a constant.

2: If ∑ F = 0, then a = 0.

The substance of first law of motion is expressed in many ways. Here, we sum them all for ready reference (for the condition that the net force on a body is zero) :

• The body may either be at rest or may move with constant velocity.
• The body is not associated with any acceleration.
• If the body is moving, then the body moves along a straight line with a constant speed without any change of direction.
• If the body is moving, then the motion of the body is an uniform linear motion.
• If a body is moving with uniform linear motion, then we can be sure that the net force on the body is zero.

First law of motion and our experience

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.