# Newton’s Laws of Motion

## What are Newton’s Laws of Motion?

Sir Isaac Newton (1642-1727) made a systematic study about motion of bodies and stated three laws of motion which are called Newton’s laws of motion.

Three Laws of motion are –

1. Newton’s First Law of motion – It states about the inertial properties of material bodies. It states the concept of force which brings any change in the state of rest or motion of a body.
2. Newton’s Second Law of motion – It states the concept of momentum of a mass body and derives the expression for magnitude of force.
3. Newton’s Third Law of motion – It states that, for every action there is an equal but opposite reaction.

### Newton’s First Law of motion

First law of Newton’s laws of motion states that –

Every body continues in its state of rest or of uniform motion in a straight line unless it is compelled by some external force to change that state.

This law of motion is consists of three parts –

FIRST PART

1. Newton’s first law states that, a body which is at rest will continue to be in rest.
2. A body in rest can’t change its state of rest by itself. This tells about a unique property of body at rest called Inertia of rest.
3. An external force is always required to make a body to move from rest.

SECOND PART

1. Newton’s first law states that, a body which is in motion will continue to be in motion with uniform speed.
2. A moving body can’t change the speed of motion by itself. This tells about a unique property of a moving body called Inertia of motion.
3. An external force is always require to make a change in speed of a moving object.

THIRD PART

1. Newton’s first law states that, a body which is in motion in a straight path will continue to be in motion in same straight path.
2. A moving body can’t change its direction of motion by itself. This tells about a unique property of moving body called Inertia of direction.
3. An external force is always require to make a change in direction of motion of a moving object.

Therefore, Newton’s first law of motion gives a definition of an external agent called a

### Newton’s Second Law of motion

Second law of Newton’s laws of motion states that –

The rate of change of linear momentum of a body is directly proportional to the applied force and this change takes place in the direction of the applied force.

Newton’s second law of motion consists of two parts –

FIRST PART

1. Newton’s second law states that the rate of change inof a body is directly proportional to the applied external force.
2. This gives expression for magnitude of a force.

SECOND PART

1. Newton’s second law states that change of momentum occurs in the direction of the applied force.
2. This gives an expression for direction of a force.

### Newton’s Third Law of motion

Third law of Newton’s laws of motion states that –

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

Newton’s third law of motion can be stated as –

1. Forces in nature always occur in pairs of bodies. Force on body A by body B is equal and opposite to the force on body B by body A.
2. In pair of forces, the two forces act simultaneously on different bodies. One of the forces is called action and the other is called reaction.
3. Since, action and reaction occur simultaneously in two different bodies, they will never cancel or balance to each other.

In other ways, Newton’s third law of motion is also stated as, to every action there is an equal and opposite reaction.

### Action & Reaction

When two bodies are in contact, then each will exert a force on the other. One of these forces is called action and the other force is called reaction.

1. Action and reaction are equal and opposite.
2. Action and reaction act simultaneously in different bodies.
3. When bodies are considered smooth, action and reaction act normal to the surfaces in contact.

## Inertia by Newton’s Laws of motion

All material bodies possess a unique quality by virtue of which they can not change their state of rest or motion by itself. This property of material body is known as inertia.

1. Inertia of a body is due to its mass content. Hence it is also called mass inertia.
2. Inertia is the property of body which produces resistance for any kind of change in the state of rest or motion.

Therefore, inertia is of two types –

1. Inertia of rest and
2. Inertia of motion.

### Inertia of Rest

According to Newton’s first law of motion, if a body is in state of rest, it will continue to be in rest till an external force is applied to change its’ state of rest.

ExampleA book kept on a table top is in rest. It will never start to move spontaneously. An external force is always require to move it from its place.

### Inertia of Motion

If a body is in state of motion, it will continue to be in state of motion with same speed and direction till an external force is applied to change the parameters of motion.

ExampleA ball is rolled on a rough tiled floor with certain velocity. It is in rolling motion and it will continue to move with same speed and in the same direction for ever, if there is no interference of any external agency. But we see that, it stops after going to some distance. This is due to the presence of surface friction, air resistance etc. which come to action and eventually ball stops.

It can be concluded that only an external agency can break the inertial state of a body. This external agency is called a force.

## Expression for Force Measurement

From Newton’s first and second laws of motion, we can define a force and derive an expression for magnitude of force.

Consider about a body of mass ( m ) moving with velocity ( \vec {v} ) then its linear momentum will be –

\text {Linear Momentum} = \text {Mass} \ \times \ \text {Velocity}

Therefore, \quad \vec p = m \vec v

Differentiating both sides with respect to time ( t ) , we get –

\left ( \frac {d \vec p}{dt} \right ) = \left ( \frac {d}{dt} \right ) \left ( m \vec {v} \right )

= m \left ( \frac {d \vec v}{dt} \right )

= m \vec {a}

Where, ( \vec {a} ) is the acceleration developed in the body.

According to Newton’s second law of motion, we have –

\text {Applied Force} \ \propto \ \text {Rate of change of momentum}

Or, \quad \vec F \propto \frac {d \vec p}{dt}

Or, \quad F \propto m \vec a

Therefore, \quad F = k \ ma Where ( k )  is a constant of proportionality.

Now, units of ( m ), \ ( a ) \ \text {and} \ ( F ) are so chosen that constant ( k = 1 )

In SI units, let –

m = 1 \ kg, \quad a = 1 \ ms^{-2} \quad \text {and} \quad F = 1 \ N

Then, \quad k = \left ( \frac {F}{ma} \right ) = \frac {1 \ N}{1 \ \text {kg} \times 1 \ \text {m s}^{-2}}

Or, \quad k = \frac {1 \ \text {kg m s}^{-2}}{1 \ \text {kg} \times 1 \ \text {m s}^{-2}} = 1

Because, absolute unit of force is \left ( 1 \ N = 1 \ \text {kg m s}^{-2} \right )

Therefore, \quad \vec F = m \vec a

From this equation, measure of force acting on a body can be obtained.

Hence, a unit force may be defined as that force which produces unit acceleration in a body of unit mass.