Newton’s Laws of Motion – Statement, Formula & Applications

A force is always needed to change the existing state of rest or motion of an object. According to Galileo, a moving object cannot change its velocity unless it is acted upon by force. An object kept at rest or executing uniform motion follows three laws of motion formulated by Sir Isaac Newton. Let us learn more about the three laws of motion.

What are Newton’s Laws of Motion?

Sir Isaac Newton gave three laws of motion that explain the relationship between the force acting on an object and the motion of the object. These three laws of motion are known as Newton’s laws of motion. Newton’s first law is also known as the law of inertia. Newton’s second law describes the relationship between applied force and the rate of change of momentum. Newton’s third law is also called the law of action and reaction.

Newton’s First Law of Motion (Law of Inertia)

Statement: An object remains in its state of rest or of uniform motion along a straight line unless compelled to change that state by an applied unbalanced force.

According to Newton’s first law of motion, a body does not change its state of rest or uniform motion unless acted upon by some unbalanced force. A net external force equal to zero cannot accelerate an object. A body by nature opposes any change in its state of rest or uniform motion along a straight line when subjected to an external force.

The tendency of a body to resist any change in its existing state of rest or motion is called inertia. The mass of an object is the measure of its inertia. The heavier the object, the more will be its inertia, and it offers more resistance to change its existing state of rest or motion. The following are the three types of inertia:

1. Inertia of Rest: It is the tendency of an object to oppose any change in its state of rest when a force is applied to it.
2. Inertia of Motion: It is the tendency of an object to oppose any change in its state of motion when a force is applied to it.
3. Inertia of Direction: It is the tendency of an object to oppose any change in its direction when a force is applied to it.

Newton’s Second Law of Motion

Statement: The rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force.

Note: Momentum is the measure of the amount of motion possessed by an object. It is equal to the product of the mass of an object and its velocity. The momentum of an object is represented by \(\rho .\) It is a vector quantity, and its SI unit is \({\rm{kg}}{\mkern 1mu} \,{\rm{m}}{{\rm{s}}^{{\rm{ – 1}}}}.\) The momentum of an object can be calculated by using the following formula:

\(\rho = m \times v\)

Where \(m\) is the mass of the object and \(v\) is the velocity of the object.

We know that a net force greater than zero can accelerate an object in its direction. It produces a change in the velocity of the object. Newton’s second law of motion describes how force depends on the change of momentum with time.

Let us assume an object of mass \(m\) is moving along a straight-line path. Let the initial velocity of the object be \(u\), and its final velocity be \(v\) on applying a force of \(F\) newtons for time \(t\). 

The initial momentum of the object \(= mu\)

The final momentum of the object \(= mv\)

The change in the momentum of the object \( = mv – mu\)

The applied force, \(F = \) rate of change of momentum

\(F \propto \frac{{mv – mu}}{t}\)

\(F = k\frac{{mv – mu}}{t} = k\frac{{m(v – u)}}{t}\)

\( \Rightarrow F = kma\)

Where \(k\) is the constant of proportionality and is equal to one, and \(a\) is the acceleration of the object.

\(F = ma\)……(i)

From equation (i), we can say that the force applied to the object is equal to the product of its mass and acceleration.

Newton’s Third Law of Motion

Statement: To every action, there is an equal and opposite reaction.

When a body exerts a force on another body, then the second body exerts an equal and opposite force at the same time on the first body. These two forces (action and reaction) always act on two different bodies. For example, when we fix a nail on a surface, the hammer exerts a force on the nail. At the same time, the nail will also exert an equal force on the hammer. These two forces are equal in magnitude but opposite in direction.

Applications of Newton’s Laws of Motion

1. Applications of Newton’s First Law of Motion
a. A pile of books placed on cardboard does not tumble when the cardboard is pulled out with a jerk because the books kept on the cardboard try to maintain their inertia of rest.
b. When a running car stops suddenly, the driver leans forward because of the inertia of motion. The lower body of the driver, being in contact with the car, immediately comes to rest, but his upper body remains in the state of motion.

2. Applications of Newton’s Second Law of Motion
a. A fielder slowly pulls his hands backwards while catching a cricket ball to increase the time during which the high velocity of moving balls reduces to zero. This decreases the acceleration of the ball, and the hands of the fielder do not get hurt.
b. If we apply more force while pedalling a bicycle, it accelerates at a higher rate.

3. Applications of Newton’s Third Law of Motion
a. A bird flying in the sky pushes the air in the downwards direction with its wings. The air exerts an equal and upward force, because of which the bird gets a lift.
b. When a person swims in a pond, he pushes the water in backward and downward directions. At the same time, the water exerts a forward force on the person, which helps him float and swim in the water.

Solved Problems Based on Newton’s Laws of Motion

Q.1. A body moving at a constant speed is made to stop in \(0.25\;{\rm{s}}\) by applying a force of \(200\;{\rm{N}}\). Calculate the initial momentum of the body.
Sol: Given, the time taken to stop the body, \(t = 0.25\;{\rm{s}}\)
The force applied to the body, \(F = 200\;{\rm{N}}\)
According to Newton’s second law of motion, the rate of change of momentum is directly proportional to the applied unbalanced force.
\(F = \frac{{{\rho _f} – {\rho _i}}}{t}\)
Where \({\rho _f}\) is the final momentum, which is equal to zero, and \({\rho _i}\) is the initial momentum of the body.
Therefore, the initial momentum of the body will be given by
\({\rho _i} = F \times t\)
\( \Rightarrow {\rho _i} = 200 \times 0.25 = 50\;{\rm{kg}}\;{\rm{m}}\,{{\rm{s}}^{ – 1}}\)

Q.2. A force of \(15\;{\rm{N}}\) acts on a body of mass \({\rm{0}}{\rm{.5}}\;{\rm{kg}}{\rm{.}}\) Find the acceleration of the body.
Sol: Given, the force acting on the body, \(F = 115\;{\rm{N}}\)
The mass of the body, \(m = 0.5\;{\rm{kg}}\)
We know that force is the product of mass and acceleration.
Therefore, the acceleration of the body will be given by
\(a = \frac{F}{m}\)
\( \Rightarrow a = \frac{{15}}{{0.5}} = 30\;{\rm{m}}\,{{\rm{s}}^{ – 2}}\)

Based on Newton’s law of motion, we can conclude that every object continues to be in its state of rest or motion unless a non-zero force acts on it. The force applied on a given mass is directly proportional to the acceleration of the object. When a body exerts a force on another body, then it will also experience a reaction of the same magnitude but opposite in direction.

Newton’s Laws of Motion FAQs

Q.1. In which situation, Newton’s laws of motion are not applied?
Ans: 1. According to Newton’s second law, the rate of change of momentum is proportional to applied force when the mass of the object is constant. So, when the object approaches the speed of light, its mass changes, and it does not obey Newton’s second law.
2. Newton’s laws of motion are not applicable in a non-inertial frame.

Q.2. What are Newton’s laws of motion used for?
Ans: Newton’s laws of motion provide a relation between the motion of the object and the applied force.  These three laws describe how much force is needed to change the state of an object, the speed and the direction of motion of the object. Newton’s laws of motion also explain the nature of force required to change the existing state of the object.

Q.3. What is Newton’s first law of motion?
Ans: Newton’s first law of motion states that an object remains in its state of rest or uniform motion along a straight line unless compelled to change that state by an applied unbalanced force.

Q.4. What are the three laws of motion called?
Ans: Sir Isaac Newton discovered three laws of motion. The first law of motion is also known as the law of inertia. The second law of motion states that the rate of change of momentum is directly proportional to the applied unbalanced force. Newton’s third law of motion is also known as the law of action and reaction.

Q.5. Why are Newton’s laws of motion important?
Ans: Newton’s laws of motion are applied to all our daily life activities. These laws explain why an object cannot move or come to rest on its own. These laws are important because they relate the object’s motion with force exerted on it and the acceleration of the object.

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