5.4 Newton’s first law of motion

What Are Newton’s Three Laws of Motion?

• Newton’s First Law of Motion (Law of Inertia)
• Newton’s Second Law of Motion (Law of Mass and Acceleration)
• Newton’s Third Law of Motion

This is illustrated in the picture below.

NEWTON’S FIRST LAW OF MOTION (Law of Inertia)

A body at rest remains at rest, and a body in motion remains in constant motion along a straight line unless acted upon by an external force.

The state of rest or uniform linear motion both imply zero acceleration. In other words we can express the first law as: If the net external force on a body is zero, its acceleration is zero. Acceleration can be non-zero only if there is a net external force on the body (Note: Inertia is a property of a body that tends to preserve that body’s state of rest when it is at rest or to maintain a body’s motion when it is in motion. The mass of the body is a measure of its inertia.).

If the sum of all the forces on a given particle \(\vec{F}\) and its acceleration is \(\vec{a}\), the above statement may also be written as
\(“ \vec{a}=0\) if and only if \(\vec{F}=0 ” .\)

Newton’s first law applies to bodies at rest and bodies in motion. Let’s look at each separately.

Body at Rest

Consider a book at rest on a horizontal surface Figure 5.1. It is subject to two external forces: the force due to gravity (i.e. its weight \(\vec{W}\) ) acting downward and the upward force on the book by the table, the normal force \(\vec{R}. \vec{R}\) (some books referred \(\vec{R} = \vec{N}\)) is a self-adjusting force. We observe the book to be at rest. Therefore, we conclude from the first law that the magnitude of \(\vec{R}\) equals that of \(\vec{W}\). We can say “Since \(\vec{W}=\vec{R}\), forces cancel and, therefore, the book is at rest”. This is incorrect reasoning. The correct statement is: “Since the book is observed to be at rest, the net external force on it must be zero, according to the first law. This implies that the normal force \(\vec{R}\) must be equal and opposite to the weight \(\vec{W}\).

Figure 5.1

Body in Motion

Consider the motion of a car starting from rest, picking up speed, and then moving on a smooth straight road with uniform speed as shown in Figure 5.2. When the car is stationary, there is no net force acting on it. This means that it will move at a constant speed in a fixed direction unless it is acted upon by a net external force. The only conceivable external force along the road is the force of friction. It is the frictional force that accelerates the car as a whole. When the car moves with constant velocity, there is no net external force.

Figure 5.2

Example 5.1: An astronaut accidentally gets separated out of his small spaceship accelerating in interstellar space at a constant rate of \(100 \mathrm{~m} \mathrm{~s}^{-2}\). What is the acceleration of the astronaut the instant after he is outside the spaceship? (Assume that there are no nearby stars to exert gravitational force on him.)

Answer: Since there are no nearby stars to exert gravitational force on him and the small spaceship exerts negligible gravitational attraction on him, the net force acting on the astronaut, once he is out of the spaceship, is zero. By the first law of motion, the acceleration of the astronaut is zero.

Example 5.2: A heavy particle of mass \(0.50 \mathrm{~kg}\) is hanging from a string fixed with the roof. Find the force exerted by the string on the particle (Figure 5.3). Take \(g=9.8 \mathrm{~m} / \mathrm{s}^2\).

Answer: The forces acting on the particle are
(a) pull of the earth, \(0.50 \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s}^2=4.9 \mathrm{~N}\), vertically downward
(b) pull of the string, \(T\) vertically upward.
The particle is at rest with respect to the earth (which we assume to be an inertial frame). Hence, the sum of the forces should be zero. Therefore, \(T\) is \(4.9 \mathrm{~N}\) acting vertically upward.