# Laws of Motion Class 11 notes Physics Chapter 5

## Introduction

When we look around us, we find the planets moving around the sun in orderly manner, movement of machinery parts in a factory, phases of the moon - all of them are following certain laws. They all are acted upon by certain forces.

In the preceding two chapters, we described motion in terms of displacement, velocity and acceleration, i.e., we used kinematic quantities for describing motion without considering what might cause that motion. In order to understand this beauty, let us take a step forward by understanding "Force and laws of motion".

## Newton’s First Law of Motion

According to this law, "A body continuous in its state of rest or constant velocity unless it is disturbed by external influence". In simple words, if no unbalanced external force acts on a body at rest, it will remain at rest and if it is moving with uniform motion, it will continue to do so. Or, if the resultant force on a body is zero, it remains unaccelerated.

### Inertia and mass

Consider two bodies of unequal masses, say a table tennis ball and a cricket ball. If both balls are pushed with equal effort for same time, a cricket ball will have much smaller velocity as compared to the other ball. Cricket ball has resisted more than table tennis ball. Or, cricket ball has larger inertia than table tennis ball. So, we can generalise, a heavier body has larger inertia than a lighter body. Larger the mass, the larger is the inertia. So, mass is a measure of inertia.

### Inertia and its Types

There are three types of inertia:

• (i) Inertia of rest
• (ii) Inertia of motion
• (iii) Inertia of direction

### 1. Inertia of Rest

It is inability of a body by virtue of which it cannot move by itself. A body at rest remains at rest and cannot start moving on its own due to inertia of rest.

### Applications

The passengers in a bus fall backward when it starts suddenly. This is because the sudden start of the bus brings motion to the bus as well as to our feet in contact with the floor of the bus. But the rest of our body opposes this motion because of inertia so they fall backwards.

### 2. Inertia of Motion

It is inability of a body in motion to stop by itself. A body in uniform motion can neither get accelerated nor get retarded on its own. It also cannot come to rest on its own.

### Applications

A man jumping from moving bus falls forward due to inertia of motion. As his feet touch the ground lower part of the body comes to rest, while the remaining parts of the body keep on moving. As a result he falls down in the direction of motion of the bus.

### 3. Inertia of Direction

It is inability of a body by virtue of which it cannot change its direction of motion by itself.

### Applications

When a car makes a sharp turn at a high speed, the driver tends to get thrown to other side due to directional inertia. When the car is moving in the straight line, the driver tends to continue in straight line motion. When the unbalanced force is applied by the engine to change the direction of motion of car. The driver slips to one side of the seat due to the inertia of his body.

## Frame of Reference

In order to describe the motion of an object, we use a specific origin with a reference system of coordinate axes called frame of reference. The frame of reference may be attached to ground, another stationary object or a moving object. We can classify the frame of reference into two categories.

• (i) Inertial frame of reference : A frame of reference attached to a stationary object or an object moving with constant velocity is called Inertial frame of reference. In such frames, Newton's laws are directly applicable.

• (ii) Non-inertial frame of reference : A frame of reference attached to an accelerated object is called non inertial frame of reference. In such frames, Newton's laws are not directly applicable.

## Momentum

It is defined as the quantity of motion contained in a body. It is measured as the product of mass of the body and its velocity and has the same direction as that of the velocity. It is a vector quantity. It is represented by p. The SI unit of momentum is kg-m/s.

p = mv

Suppose you catch a cricket ball and a tennis ball when dropped from same height. We find that it is easier to catch a tennis ball than the cricket ball. This determines that mass is an important factor that determines the effect of force on its motion.

## Force

When we look around us and observe state of rest or motion of bodies, we find that nothing moves on its own. When we push or pull a body

1. It may change its state of rest or of uniform motion.
2. It may change its direction of motion.
3. It may change its shape.

We say that we exert a force on a body if we push or pull it. This push or pull may be gentle or hard, so force has a magnitude. This push or pull may be in different directions, so force has a direction. It means force is a vector quantity. The SI unit of force is newton represented by 'N'. The CGS unit of force is Dyne.

Note : 1N = 105 dyne

Force is an entity which when applied on a body changes or tends to change a body’s, State of rest, State of uniform motion, Direction of motion, Shape.

(i). Balance Force : When a number of forces acting simultaneously on a body do not bring about any change in its state of rest or of uniform motion along a straight line, then the forces acting on the body are said to be balanced forces. Balanced forces do not produce any acceleration.

(ii). Unbalanced Force : When a number of forces acting simultaneously on a body bring about a change in its state of rest or of uniform motion along a straight line, then these forces acting on the body are said to be unbalanced forces. To accelerate an object, an unbalanced force is required.

(iii). Resultant Force : When two or more forces act on a body simultaneously, then the single force which produces the same effect as produced by all the forces acting together is known as the resultant force.

## Newton's Second Law of Motion

This law states that "The rate of change of momentum of a body is directly proportional to the applied force and it takes place in the direction in which the force acts.”

### Mathematical Formulation of Second Law

Consider a body of mass m moving with some initial velocity v. If an unbalanced force F is applied, the velocity will change from v to v + Δv. The change in momentum will be Δp = mΔv which changes from p (initial momentum) to p + Δp (final momentum).

According to the second law,

\vec{F}\propto\frac{d\vec{P}}{dt}   ,    \vec{F}=\frac{d\vec{P}}{dt}

The momentum of a body is defined as,

\vec{P}=m\vec{v}

\therefore\frac{d\vec{P}}{dt}=\frac{d(m\vec{v})}{dt}

\vec{F}= m\frac{d\vec{v}}{dt}

\vec{F}= m\vec{a}

### Application of Newton's Second Law of Motion

1. Cricket player lowers his hand while catching the ball : The player increases the time during which the high velocity of moving ball reduces to zero. If we increase t, F decreases, so force of impact on palm of the fielder reduces.

2. A karate player can break a pile of tiles with a single blow of his hand : Because he strikes the pile of tiles with his hand very fast, during which the entire momentum of the fast moving hand is reduced to zero in very short interval of time. This exerts a very large force on the pile of tiles which is sufficient to break them, by a single blow of his hand.

3. In a high jump athletic event, the athletes are allowed to fall either on a sand bed or cushioned bed : This is because to increase the time of athletes fall to stop after making the high jump, which decreases rate of change of momentum and decreases force of impact.

## Impulse

The product of force and time, which is the change in momentum of the body remains a measurable quantity. This product is called impulse.

Impulse = Force × time duration

= Change in momentum

## Newton's third Law of Motion

According to this law, "To every action there is always equal and opposite reaction".

Let two bodies 1 & 2 are interaction together, then

F12 = -F21

(force on body 2 by 1) = -(force on body 1 by 2)

If masses of both bodies be m1 & m2 then

m_{1}(\frac{dv_1}{dt})=m_{2}(\frac{dv_2}{dt})

### Action and Reaction

When there is a force exerted by body I on body II, there is also a force exerted by body II on body I. These forces are equal in magnitude and act in opposite directions. Such a pair of forces is called an action-reaction pair. Any of the two forces may be called the action, the other will be the reaction.

### Applications of Third Law

• Recoiling of a gun : When a bullet is fired from a gun, it exerts a forward force on the bullet and the bullet exerts an equal and opposite force on the gun. Due to high mass of the gun, it moves a little distance backward and gives a backward jerk to the shoulder of the gunman.

• To walk, we press the ground in backward direction with foot : When we walk on the ground, our foot pushes the ground backward and in return the ground pushes our foot forward.

## Significance of Newton’s Laws

1. The first law talks about the natural state of motion of a body, i.e., motion along a straight line with constant speed.

2. The second law says that if a body is not following its natural state of motion, then there has to be a net unbalanced external force acting on the body.

3. The third law talks about the nature of the force, i.e., forces exist in pairs.

## What is Pulley?

It is a simple wooden or metallic machine that uses a wheel and rope to lift heavy loads. Let a be the common acceleration of the system of two bodies, which is given by

a=\frac{(m_{1}-m_{2})g}{m_1+m_2}

### (i). Fixed Pulley

When the block of the pulley is fixed on a high platform, it is known as fixed. An extensible string passes over the groove where its one end is attached to the body to be lifted while the other end is free.

### (ii). Movable Pulley

When the block of the pulley is not fixed but carries the load, it is known as Movable. An inextensible string is tied around the groove where its one end is fixed to fixed support while the other end is kept free to apply the effort.

## FAQs

Que:- Can we say that first law can be derived from second law?
Ans:- No, three laws are independent.

Que:- Can we say that action occurs before the reaction?
Ans:- No, both occur at the same time.

Que:- Can we say that action and reaction act on the same body?
Ans:- No, they always act on different bodies.

## Conservation of Momentum

According to conservation law of linear momentum, “The total momentum of an isolated system of interacting particles is conserved.” In other words, “for an isolated system the initial momentum of the system is equal to the final momentum of the system”.

Consider two objects A and B of masses m1 and m2 moving along the same direction at different velocities u1 and u2 respectively.

m1u1 + m2u1 = m1v1 + m2v2

Total momentum before collision = Total momentum after collision

### Applications of Law of Conservation of Linear Momentum

• (i) Recoil Velocity of a Gun
• (ii) Rocket propulsion

## Various Forces in Nature

In mechanics, we come across a variety of forces, like the weight of a body or the force exerted by a stretched spring.

### (i). Weight

Weight is the gravitational force with which the earth pulls an object. The weight of an object is (F=mg), where g is acceleration due to gravity. The weight of a body is a force acting on the body towards the centre of earth.

### (ii). Normal Reaction

Normal reaction is a force between two surfaces in contact. This force is normal (perpendicular) to the surfaces in contact. This force develops when a surface comes in contact with another surface. Such forces which develop on contact, are called contact forces. Normal reaction occurs to stop two bodies in contact to merge into each other.

### (iii). Tension

It is the pulling force exerted by a string, along the length of the string on the objects connected to the string. If string is massless then magnitude of tension is same throughout the string.

### (iv). Spring Force

A spring is generally a helical metallic wire. When the two free ends of the spring are pulled away or pushed towards each other, the length of the spring is changed. The spring has a tendency to come back to its original length or it develops an opposition to change in its length. This opposing force (F) is the restoring force.

The opposing force is directly proportional to the change in length. It is given by F = kx, where k is a constant for a given spring.

## Friction

It is a general observation that when you try to slide a heavy box across the floor, the box does not move at all unless you push it with a certain minimum force. This means that there exists a certain opposition to the motion of box on the ground. This opposing force acts between the surface of box and ground and is called force of friction.

### Factors Affecting Friction

• Nature of the medium of contact between two bodies
• Normal reaction
• Area of contact

### Type of Friction

#### (i). Kinetic Friction

The kind of friction that acts when a body slides over a surface is called a kinetic friction force. The magnitude of the kinetic friction force usually increases when the normal force increases. This is why it takes more force to slide a box full of books across the floor than to slide the same box when it is empty.

The magnitude of the kinetic friction force fk is found experimentally to be approximately proportional to the magnitude N of the normal force. In such cases, we represent the relationship by the equation

fk = μkN

where μk is a constant called the coefficient of kinetic friction.

#### (ii). Static Friction

The frictional forces between two surfaces in contact before a relative motion has started, are referred to as static friction. Static friction is always a little more than dynamic friction.

The magnitude of static frictional force is also proportional to normal force.

fs = μsN

### Limiting Frictional Force

Limiting friction is defined as the maximum value of static friction that comes into play when the body is just at the point of sliding over the surface of another body. This frictional force acts when body is about to move. This is the maximum frictional force that can exist at the contact surface.

### Laws of Friction

1. The magnitude of limiting frictional force is proportional to the normal force at the contact surface.
2. The magnitude of limiting frictional force is independent of area of contact between the surfaces.

### Angle of Repose (θ)

It is the maximum angle of inclination (θ) of a rough inclined plane with horizontal such that the block kept on it remains at rest.

At angle of repose,

Driving force = Limiting friction

mg sin θ = μsN

mg sin θ = μs mg cos θ

tan θ = μss

Angle of friction = Angle of repose

### Rolling Friction

When a spherical body or a circular ring rolls over a horizontal plane without slipping then applied friction by the surface on body is called rolling friction. Rolling friction is much smaller than static or sliding friction. That is why, discovery of the wheel was a major milestone in the history.

### Methods to reduce friction

Following are the different methods that are used for reducing the friction:

1. For objects that move in fluids such as boats, planes, cars, etc, the shape of their body is streamlined in order to reduce the friction between the body of the objects as the fluid.

2. By polishing the surface, as polishing makes the surface smooth and friction can be reduced.

3. Using lubricants such as oil or grease can reduce the friction between the surfaces.

4. When objects are rolled over the surface, the friction between the rolled object and surface can be reduced by using ball bearings.

## Pseudo-Force

A Pseudo force (also called a fictitious force, inertial force or d’Alembert force) is an apparent force that acts on all masses whose motion is described using a non-inertial frame of reference frame, such as rotating reference frame.

## Summary

• Resultant force : When two or more forces act on a body simultaneously, then the single force which produces the same effect as produced by all the forces acting together is known as the resulting force.

• Balanced force : When different forces acting on a body give a zero resultant, then the forces are said to be balanced.

• Unbalanced force : When net force on the body is not equal to zero, then the body is said to have unbalanced force.

• Inertia : The tendency of a body to maintain its state of rest or of uniform motion is known as inertia.

• Momentum : It is defined as the quantity of motion contained in a body. It is the product of mass and velocity.

• Force : It is defined as the rate of change of momentum.

• One newton : It is that force which when acting on a mass of 1 kg produces in it an acceleration of 1 m/s2 in its direction.

• Impulse : It is defined as change in momentum.

• Friction : It is a contact force which opposes the relative motion of a body.

• Static friction : The force of friction which comes into play between the surfaces of two bodies before the body actually starts moving is called static friction.

• Limiting friction : It is the maximum value of static friction which comes into play when a body is just about to slide over the surface of another body.

• Kinetic friction : Force of friction acting between the two surfaces, when one surface is in steady motion over the other surface is called kinetic friction.

• Banking of roads : The phenomenon of raising outer edge of the curved road above the inner edge is called banking of curved road.

• Newton’s first law : A body remain in its state of rest or of uniform motion along a straight line unless acted upon by some unbalanced external force to change that state of rest or of uniform motion.

• Newton’s second law : The rate of change of momentum of a body is directly proportional to the applied unbalanced external force and it is in the direction of the resultant force.

• Newton’s third law : In any interaction between two bodies, the force exerted by the first body on the second is equal and opposite to the force exerted by the second body on the first.

• Conservation of linear momentum : If there is no net external force acting on the system, the total momentum remains conserved.

• Equilibrium of a particle : In mechanics, a body is in equilibrium when it is at rest or moving with constant velocity in an inertial frame of reference.