Newton’s Laws of Motion

For centuries physicists have been trying to understand the mechanics of nature and the things around us. Aristotle, the famous Greek thinker, had formulated certain ideas of motion. Eventually, Galileo came up with the idea of inertia which proved Aristotle’s mechanics wrong. Physicist Isaac Newton built on Galileo’s ideas to create the famous three laws of motion called Newtons laws of motion. In this article, we will look at these Newtons laws in detail.

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Newton’s First Law of motion

Newton’s first law of motion is based on Galileo’s law of inertia. Galileo had observed that a body does not change its current state (of rest or uniform motion) unless an external unbalanced force compels it to do so. Based on this, Newton’s First Law of motion states:

“A body continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise.”

Whether a body is in a state of rest or uniform motion, the acceleration is zero. Hence, Newton’s First Law can also be written 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.”

There are two scenarios to consider:

• We know that the net external force on a body is zero
• We don’t know if the net external force is zero but the body is un-accelerated

Browse more Topics under Laws Of Motion

• Circular Motion
• Common Forces in Mechanics
• Solving Problems in Mechanics

Case I. Net external force on a body is zero

If we know that the net external force on a body is zero, then we can conclude that it has zero acceleration.

Example 1

Imagine a spaceship in space, away from all other objects and its rockets turned off. In space, there are no external forces acting on it. Hence, by Newton’s First Law, the spaceship’s acceleration is zero. So, if it is in motion, then it will continue to move with a uniform velocity.

Case II. We don’t know if the net external force is zero but the body is un-accelerated

It is very difficult to understand all the forces that act on a body at a given time. However, if we know that the body is either at rest or in uniform linear motion (un-accelerated), then we can conclude that the net external force acting on the body is zero.

On Earth, gravity affects all bodies. Also, bodies in motion can experience friction, viscous drag, etc.  So, if a body is at rest or in a state of uniform linear motion on earth, then it is because the different external forces acting on it add up to zero.

Example 2

Imagine a book at rest on a horizontal table as shown below:

There are two external forces acting on this book:

• Gravity or its weight (W), acting downward
• Normal Force (R), acting upward. R is also a self-adjusting force.

We are not aware of all the forces acting on the book but we know that it is at rest. Therefore, using Newton’s First Law, we can conclude that R is equal to W. Hence, we state: ‘According to Newton’s First Law of motion since the book is at rest, the net external force acting on it must be zero. Hence, the normal force is equal and opposite to the weight (W).

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Newton’s Second Law of motion

Before we look at the first law, let’s understand the concept of Momentum.

Momentum

The momentum of a body is the product of its mass and velocity.

p = mv … (1)

where p = momentum, m = mass of the body, and v = velocity of the body. Momentum is a vector quantity; it is direction dependent. It is an important quantity in the study of the effect of force on the motion. Here are some examples:

• If a light and heavy vehicle are parked on a horizontal road and need to be pushed to bring them into motion, then the heavier vehicle will need much greater force than the lighter vehicle to bring both of them to the same speed in the same time period. Also, to stop these vehicles, a greater opposing force is needed to stop the heavier one.
• What happens when you fire a bullet from a gun on a man? The bullet will pierce his tissues before coming to a stop, right? What happens if the same bullet is fired at half the speed? It might not cause so much damage. Hence, for the same mass, a greater opposing force is needed to stop the body if it is moving at a greater speed.

If we take these two examples together, then we can conclude that the mass and speed are relevant variables of motion.

Observation

An observation worth noting is that if you apply the same force to two bodies having different masses, then the lighter body will pick up more speed initially but eventually both the bodies will acquire the same momentum.

• Imagine rotating a stone in the air with the help of a string, in a horizontal plane with a uniform speed. Since the mass and speed of the stone is the same, its momentum is fixed. However, its direction changes causing a change in the momentum vector. Hence, a force needs to be exerted by your hand to keep the stone in a circular motion.

Based on these observations, Newton formulated the Second Law of Motion:

“The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.”

This law is represented by the equation F = kma, where F is the net external force acting on a body, k is the constant of proportionality, m is the mass of the object, and a is the acceleration. In the SI system, one unit force is one that causes an acceleration of 1 m/s² to a mass of 1 kg. This unit is called Newton. Therefore, 1N = 1 kg m/s².

Points to Remember

• Internal forces are not included in F.
• Acceleration is not determined by the history of motion
• If F = 0, the acceleration (a) is also zero. Hence, the second law is consistent with the first law.
• This is a vector law and can be broken down into three equations for three vector components.

Newton’s Third Law of motion

While the second law relates the external force on a body with its acceleration, one question that remains unanswered is the origin of the external force on the body. According to Newtonian mechanics, the external force always arises due to some other body.

According to Newton, force can never occur singly in nature; it is the mutual interaction between two bodies. This formed the basis of Newton’s Third Law of motion which states:

“To every action, there is always an equal and opposite reaction.”

Here are some points to remember about the Third Law:

• Forces always occur in pairs. The force exerted by an object A on an object B is equal and opposite to the force exerted on A by B.
• There is no cause-effect relation implied by the law. For that matter, the force on A by B and that on B by A are exerted at the same instant.
• These forces apply to two different bodies. However, if two bodies are components of a system, then they can add up to give a null force.

Now let’s looks at some more examples on Newtons Laws studied above.

Solves Examples on Newtons Laws

Q1. Give the magnitude and direction of the net force acting on:

1. A drop of rain falling down at a constant speed,
2. A cork of mass 10 g floating on water,
3. Kite skilfully held stationary in the sky,
4. Car moving with a constant velocity of 30 km/h on a rough road,
5. A high-speed electron in space far from all material objects, and free of electric and magnetic fields.

Solution:

1. Since the raindrop is falling at a constant speed, its acceleration is zero. Hence, according to Newton’s Second Law, the net force acting on the raindrop is zero.
2. The weight of the cork is acting in the downward direction and the buoyant force of the water is exerted in the upward direction. Hence, the net force is zero.
3. Since the kit is stationary in the sky, Newton’s First Law implies that no net external force is acting on the kite.
4. Since the velocity of the car is constant, there is no acceleration of the car. Hence, as per Newton’s Second Law, the net force acting on the car is zero.
5. Since the high-speed electron is free from all fields, the net force acting on it is zero.

This concludes our discussion on the topic Newtons Laws of Motion.