# Law of Motion : Newton’s Laws of Motion

## LAWS OF MOTION

Newton’s laws of motion are three physical laws that, together, laid the foundation for classical mechanics.

### Frame of reference:-

A “frame of reference” is just a set of coordinates: something you use to measure the things that matter in Newtonian problems, that is to say, positions and velocities, so we also need a clock. Or A place and situation from where an observer takes his observation is called frame of reference.

A point in space is specified by its three coordinates (x, y, z) and an “event” like, say, a little explosion, by a place and time: (x, y, z, t).

An inertial frame” is defined as one in which Newton’s law of inertia holds—that is, anybody which isn’t being acted on by an outside force stays at rest if it is initially at rest, or continues to move at a constant velocity if that’s what it was doing to begin with. Example of inertial frame of reference is observer on Earth for all motion on surface of earth. Car moving with constant velocity

An example of a non-inertial frame is a rotating frame, such as an accelerating car,

Accelerated frame of reference” is defined as one in which Newton’s law of inertia does not hold good. Example When bus starts suddenly from rest we experience backward jerks, although no force is acted on us.

Any frame of reference which is moving with acceleration are called accelerated frame of reference.

### Newton’s first law of motion

If a body is observed from an inertial frame which is at rest or moving with uniform velocity then it will remain at rest or continue to move with uniform velocity until an external force is applied on it The property due to which a body remains or continues its motion with uniform velocity is called as inertia Force is a push or pull that disturbs or tends to disturb inertia of rest or inertia of uniformmotion with uniform velocity of a body.

Hence first law of motion defines inertia, force and inertial frame of reference.

The inertia is of three types

It is the inability of the body to change its state of rest by itself.

(a) A person standing in a bus falls backward when the bus suddenly starts moving. This is because, the person who is initially at rest continues to be at rest even after the bus has started moving.

(b) A book lying on the table will remain at rest, until it is moved by some external agencies.

(c) When a carpet is beaten by a stick, the dust particles fall off vertically downwards once
they are released and do not move along the carpet and fall off.

Inertia of motion is the inability of the body to change its state of motion by itself.

(a) When a passenger gets down from a moving bus, he falls down in the direction of the motion of the bus.

(b) A passenger sitting in a moving car falls forward, when the car stops suddenly.

(c) An athlete running in a race will continue to run even after reaching the finishing point

It is the inability of the body to change its direction of motion by itself.

When a bus moving along a straight line takes a turn to the right, the passengers are thrown towards left. This is due to inertia which makes the passengers travel along the same straight line, even though the bus has turned towards the right.

## Force

From the first law, we infer that to change the state of rest or uniform motion, an external agency called, the force is required.

Force is defined as that which when acting on a body changes or tends to change the state of rest or of uniform motion of the body along a straight line.

A force is a push or pull upon an object, resulting in the change of state of a body. Whenever there is an interaction between two objects, there is force acting on each other. When the interaction ceases, the two objects no longer experience a force. Forces exist only as a result of an interaction.

There are two broad categories of forces between the objects, contact forces and non–contact forces resulting from action at a distance.

Contact forces are forces in which the two interacting objects are physically in contact with each other.

Tensional force, normal force, force due to air resistance, applied forces and frictional forces are examples of contact forces.

Action-at-a-distance forces (non- contact forces) are forces in which the two interacting objects are not in physical contact which each other, but are able to exert a push or pull
despite the physical separation.

Gravitational force, electrical force and magnetic force are examples of non- contact forces.

### Newton’s second law of motion:-

Newton’s second law of motion deals with the behaviour of objects on which all existing forces are not balanced.

According to this law, the rate of change of momentum of a body is directly proportional to the external force applied on it and the change in momentum takes place in the direction
of the force.

If p is the momentum of a body and F the external force acting on it, then according to Newton’s second law of motion

Unit of force is chosen in such a manner that the constant k is equal to unity. (i.e)

If a body of mass m is moving with a velocity v then, its momentum is given by

Here a is the acceleration produced in the body given by

a=dv/dt
The force acting on a body is measured by the product of mass of the body and
acceleration produced by the force acting on the body.

The second law of motion gives us a measure of the force. The acceleration produced in the body depends upon the inertia of the body (i.e) greater the inertia, lesser the
acceleration.

One Newton is defined as that force which, when acting on unit mass produces unit acceleration. Force is a vector quantity. The unit of force is kg m s−2 or Newton. Its dimensional formula is MLT−2

(i) Impulsive Force
An impulsive force is very great force acting for a very short time on a body, so that the change in the position of the body during the time the force acts on it may be neglected.
(e.g.) The blow of a hammer, the collision of two billiard balls etc.

(ii) Impulse of a force
The impulse J of a constant force F acting for a time t is defined as the product of the force and time.

(i.e) Impulse = Force × time
J = F × t
The impulse of force F acting over a time interval t is defined by the integral,

j = ∫ . − − − − − (1)
The impulse of a force, therefore can be visualized as the area under the force versus time graph as shown in Fig.

When a variable force acting for a short interval of time, then the impulse can be measured as,

J = Faverage × dt
Impulse of a force is a vector quantity and its unit is N s.

### Principle of impulse and momentum;

By Newton’s second law of motion, the force acting on a body = m a
where m = mass of the body and
a = acceleration produced
The impulse of the force =

If u and v be the initial and final velocities of the body then, a = (v-u)/t

Therefore, impulse of the force =

= ×( − )/

= ( − ) = −

Impulse = final momentum of the body – initial momentum of the body.

(i.e) Impulse of the force = Change in momentum

The above equation shows that the total change in the momentum of a body during a time interval is equal to the impulse of the force acting during the same interval of time. This is
called principle of impulse and momentum

(i) A cricket player while catching a ball lowers his hands in the
direction of the ball.

If the total change in momentum is brought about in a very short interval of time, the average force is very large according to the equation,

= − /

By increasing the time interval, the average force is decreased. It is for this reason that a cricket player while catching a ball, to increase the time of contact, the player should lower his hand in the direction of the ball , so that he is not hurt.

(ii) A person falling on a cemented floor gets injured more where as a person falling on a sand floor does not get hurt. For the same reason, in wrestling, high jump etc., soft ground
is provided.

(iii) The vehicles are fitted with springs and shock absorbers to reduce jerks while moving on uneven or wavy roads.

### Newton’s third Law of motion:-

It is a common observation that when we sit on a chair, our body exerts a downward force on the chair and the chair exerts an upward force on our body.

### There are two forces resulting from this interaction:

A force on the chair and a force on our body. These two forces are called action and reaction forces. Newton’s third law explains the relation between these action forces.

It states that for every action, there is an equal and opposite reaction.
(i.e.) whenever one body exerts a certain force on a second body, the second body exerts an equal and opposite force on the first.

Newton’s third law is sometimes called as the law of action and reaction. Let there be two bodies 1 and 2 exerting forces on each other.

Let the force exerted on the body 1 by the body 2 be F12 and the force exerted on the body 2 by the body 1 be F21

Then according to third law of motion

One of these forces, say F12 may be called as the action whereas the other force F21 may be called as the reaction or vice versa.

This implies that we cannot say what the cause (action) is or which the effect (reaction) is. It is to be noted that always the action and reaction do not act on the same body; they always act on different bodies.

The action and reaction never cancel each other and the forces always exist in pair.

The effect of third law of motion can be observed in many activities in our everyday life.

(i) When a bullet is fired from a gun with a certain force (action), there is an equal and opposite force exerted on the gun in the backward direction (reaction).

(ii) When a man jumps from a boat to the shore, the boat moves away from him. The force he exerts on the boat (action) is responsible for its motion and his motion to the shore is due to the force of reaction exerted by the boat on him.

(iii) The swimmer pushes the water in the backward direction with a certain force (action) and the water pushes the swimmer in the forward direction with an equal and opposite force (reaction).

(iv) We will not be able to walk if there were no reaction force. In order to walk, we push our foot against the ground. The Earth in turn exerts an equal and opposite force.

This force is inclined to the surface of the Earth. The vertical component of this force balances our weight and the horizontal component enables us to walk forward.

This post was all about Newton’s Laws of Motion including Newton’s first law of motion, Newton’s second law of motion, Newton’s third law of motion. This will help you on exams. Like our page on page and Join group for daily dose of Informations.