Newton's First Law of Motion

A nonzero net force causes the change in motion of a body. What happens when there is no net force on a body? The answer of this question is given by Newton's first law. Newton's first law determines what happens to a body if there is no net force on the body (you'll see later how we change the statement slightly to define force using Newton's first law).

NEWTON'S FIRST LAW: A body initially at rest always remains at rest and a body initially in motion always keeps moving with constant velocity if no net external force acts on the body.

If there is no net force on a body, the body always remains in its current state either at rest if it was initially at rest or moving if it was initially in motion. We just stated Newton's first law of motion where we said "body at rest" which is not necessary as a body with zero velocity is the same thing as being at rest. An alternative statement can be

NEWTON'S FIRST LAW: A body has constant velocity (can be zero) if no net external force acts on it.

Here we said "no net force" which is the same as no forces at all, that is in the absence of any forces or multiple forces cancel out to zero. To be able to define force only using Newton's first law we must consider an isolated system where no forces act on a body at all, that is the same as the absence of all forces.

NEWTON'S FIRST LAW: A body has constant velocity in the absence of any external forces.

The statement just stated transfers the case what happens if net force is zero to Newton's second law. In other words this statement lets Newton's second law to handle the situation of multiple forces acting on a body cancel to zero focusing completely on an isolated system without any forces at all (absence of all forces).

Newton's second law can handle the situation of zero net force (there are multiple forces but they cancel to zero) but you'll see it'll be converted back to Newton's first law, so we stick to the Newton's first law of motion for zero net force as well.

It's obvious from the above statement of Newton's first law that only a force can cause the change in motion of a body.

FORCE: A force is an interaction which causes the change in motion of a body.

The isolated system of no forces at all we considered in the statement of Newton's first law above is equivalent to zero net force, that is multiple forces exist but they cancel to zero. In real life situations where multiple forces on a body cancel to zero, only a nonzero net force can cause the change in motion and zero net force is equivalent to no forces at all.

Applying zero net force, that is multiple forces cancel to zero is equally valid in Newton's first law of motion and zero or no net force is equivalent to the absence of all forces on a body.

If a body has a constant velocity (can be zero), the body is said to be in equilibrium. A constant velocity tells everything, sure it can be zero which determines the state of rest and nonzero constant velocity means uniform motion. This eventually means a body initially at rest remains at rest and a body initially in motion remains in motion if there is no net force on the body and the body is said to be in equilibrium.

Newton's first law is the equilibrium condition of a body. A body can be said to be in equilibrium if no forces act on the body at all or the vector sum of all forces on the body is zero (zero net force).

Remember the constant velocity means constant speed along straight line and the change in motion is the change of velocity. Velocity is a vector quantity and if it changes there must be a force. Newton's first law does not tell that a body in uniform circular motion (motion with constant speed in a circle) is acted on by no force. The direction of velocity always changes, that is the motion changes and there must be a force.

Inertial Frame of Reference

Newton's first law is incomplete if we don't include inertial frame of reference in our statement of Newton's first law. To understand what inertial frame of reference is we begin with an example.

You are travelling in a bus moving with constant velocity at the back seat and there is a ball on the floor sitting next to you. If the driver applies brakes, the ball moves towards the front of the bus, not only the ball moves you also move forward. Why do you think there are seat belts in a car? Let's move back to the bus example and focus on the ball only for now.

When the ball moved, you didn't see any force applied on the ball but the ball moved why? Initially the ball was in motion with the bus, when the bus tried to stop the ball didn't want to come to rest due to the inertia of motion and you saw the ball moved even without any force applied on it inside the bus.

No force was ever applied on the ball, the force was only applied to stop the bus not the ball but inside the bus you see the ball (which was already in motion with the bus) moving from rest without any force being applied on it which completely violates the Newton's first law of motion.

The Newton's first law of motion is no longer valid when the driver applies breaks inside the bus, any object should not be moving from rest without force. So you can understand that the Newton's first law in invalid in an accelerated system.

The frame of reference in which Newton's first law is valid is called inertial frame of reference.

The frame of reference of the bus at the time when the bus tried to stop (accelerated system) is no longer an inertial frame. If the bus was moving with constant velocity, the bus would be an inertial frame and Newton's first law would be valid.

So an accelerated system is not an inertial frame. The Earth is not completely an inertial frame due to acceleration associated with its rotation but we can say the Earth is approximately an inertial frame.

Newton's first law is valid only in an inertial frame of reference, so the final statement of Newton's first law can stated as

NEWTON'S FIRST LAW: When viewed from inertial frame of reference, a body has constant velocity if no net external force acts on it.

No net force or zero net force mean both multiple forces that cancel to zero and the absence of all forces on a body. In real life situations we find systems where multiple forces cancel to zero which results equilibrium and we describe such situation with Newton's first law.

Mechanics
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