What is motion?

If a very smooth ball is rolled down an inclined surface with zero friction, the ball will continue to roll indefinitely for an infinite time, in an attempt to reach to the same height on the opposite hill!

If the mass of a ball is at rest, it will continue to be at rest for an indefinite time. On the other hand, if the mass of a ball is moving on a smooth surface with zero friction in uniform motion in a fixed direction, then it will continue to do so for an indefinite time period. Both these scenarios are true, provided the mass of ball is under the action of zero force. This is the famous thought experiment by the famous scientist Galileo, which subsequently led to Newton’s first law of motion.

Do you think it is possible to have a motion in the absence of a force? Or do you think it is possible to have force without motion in the body?

The answer to both these counter statements is yes!

Motion in itself does not require force. As per Newton’s first law, a body continues to be in uniform motion unless an external force is applied. As a counter statement, if the net resultant of a system of forces on the body is zero, then the body remains at rest.

Newton’s first law tells us that the velocity of a body does not change if no external force acts on it. The law also implies that if a net external force acts on a body, a change in motion of the body will occur.

In Sir Isaac Newton’s own words, the first law states:
Every body continues in its state of rest, or uniform motion in a straight line, unless compelled to change the state by force impressed upon it.

State of Equilibrium

This motion may be considered a combination of translational and rotational motions. A single force acting on a body may produce change in both these motions of the body. However, when multiple forces act on the body, their effects can compensate each other, resulting in no change in its translational or rotational motion. When this happens, the body is said to be in equilibrium.

For a body in equilibrium, if the vector sum of the multiple forces acting on the body is zero, then the body is said to be in translational equilibrium. On the other hand, if the force(s) acting on the body has no tendency to produce any rotation in the body, then the body is said to be in rotational equilibrium.

The statement that a body is in complete equilibrium, when both these conditions are satisfied, is the essence of Newton’s first law of motion. Greater the mass of a body, more is the force required to disturb the body out of its state of rest or uniform motion; or more the mass of the body, greater is the force required to move it out of either of its two natural states—state of rest and state of uniform motion.

Examples of Newton’s First Law

The application of Newton’s first law implies the definition of inertial reference system. To understand, let us look at an example.

Suppose we are sitting in a train moving along a straight track at a constant speed. A smooth plastic puck is lying on the smooth floor of the train. You observe that the puck is stationary on the floor of the train, moving at constant velocity, thereby obeying Newton’s first law.  What if the train suddenly picks speed? What do you observe of the puck on the floor? The puck begins to slide backwards, opposite to the motion of the train.

The train in the above instance represents an inertial reference frame as long as it moves at a constant velocity. The puck on the floor remains at rest and obeys Newton’s first law. When the train begins to accelerate, it is called a non-inertial reference frame. According to the person sitting in the accelerated train, there is no force on the puck, but he sees the puck accelerate from rest and move backwards. Thereby, the Newton’s first law is violated in accelerated or non-inertial reference frames.

Let’s consider another example. Suppose you are sitting in a moving car driven by your friend, at a constant velocity. You see that your body and the interior of the car are at rest with respect to each other. Since there is no net force on you or the moving car, you see yourselves at rest as compared to the inside of the car. This is according to Newton’s first law of motion. Now, suddenly your friend presses the accelerator and you begin to sense a force that presses you against the seat, you experience a force acting on your body. But when you look around , in the car, everything is still at rest—the interior of the car and your friend too! According to Newton’s first law, a change was expected as soon as a force started to act on you, but nothing changed  inside the car. Clearly, Newton’s first law is violated here!

The car behaved as an inertial reference frame as long as it was moving with constant velocity, that is, uniform motion. The law is followed in inertial reference frames, but an accelerating car behaves as a non-inertial reference frame. Thus, it is the reference frame of observation with an acceleration, wherein Newton’s first law of motion is not followed.

Is Earth an inertial or a non-inertial reference frame?

Earth revolves around the Sun in almost a circular path under the effect of the Sun’s force of gravitation, and it experiences centripetal acceleration toward it. Note that the Earth and every other planet also exert equal force of gravitation on the Sun. Additionally, Earth also rotates on its axis once a day, that is, every 24 hours. Any point on the surface of the equator experiences an additional centripetal acceleration toward the center of Earth.

 
 In reality, these two accelerations are very small when compared to g (the acceleration due to gravity) on Earth. These accelerations can safely be ignored. Hence, the reference frames on or near the surface of Earth are considered as inertial frames of reference, on which Newton’s first law is always obeyed. In other words, all the Newton’s laws of motion, the first, second and third law, apply in inertia frames of reference.

Pitfall prevention

Newton’s first law does not say what happens with an object with zero net force, that is, multiple forces that cancel each other; it explains what happens in the absence of a force on the body. The role of force should be well understood. Do not assume that  “force is the cause of the motion.” Remember that a body can be in motion in the absence of forces as described by Newton’s first law of motion. It must be well understood that “force is the cause of changes in motion.”

Let’s explore some common examples and try to recognize whether they represent inertial or non-inertial reference frame. Just to reiterate, a frame of reference is just a viewpoint from where the position and the velocity of an object are observed.

In each of the examples below, identify if the suggested frame is inertial or non-inertial.  Justify your response based on the applicability of Newton’s first law.

Any reference frame or a body to constitute an inertial reference frame should be in uniform motion, that is, in a non-accelerated motion. Only under such conditions will Newton’s first law be applicable. On the other hand, any reference frame or a body to constitute a non inertial reference frame should be in a nonuniform motion, that is, accelerated motion.

We shall discuss Newton’s second law and third law in subsequent articles.

Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for 

• Bachelors in Science (Physics) 
• Masters in Science (Physics) 

Practice Problems

Q1. Newton’s first law does not say what happens for an object with zero net force, rather it says what happens in the absence of the force.

1. True
2. False

Answer: True

Q2. It is not possible to either have motion in the absence of force or have force in the absence of motion.

1. True
2. False

Answer: False

Q3. If a single force acts on an object, it implies that the object must accelerate.

1. True
2. False

Answer: True

Q4. If an object does not experience any acceleration, it implies that NO force acts on it.

1. True
2. False

Answer: False

Q5. The acceleration of an inertial reference frame is zero, so it moves with a constant velocity.

1. True
2. False

Answer: True