Force and Laws of Motion : Notes, Class 9 Science PDF Download

 Page 1


 
 
FORCE AND LAWS OF MOTION
A body at rest can be moved and one that is moving can be 
brought to rest. What makes bodies to move or change their 
direction of motion or stop, if they are moving?  We can say 
that it is a push or pull applied to the objects make them move 
or stop or change their shape.  The push or pull is actually the 
force applied in any way. Therefore we can define force as: –  
Force is an influence which tends to set a stationary 
body in motion or change the speed and direction of a 
moving body or change the shape of a body. Force is a 
vector quantity; it is having magnitude as well as 
direction. 
 
Effects Of Force 
1. Force can move a body at rest. 
2. Force can accelerate or decelerate a body. 
3. Force can change the direction of motion. 
4. Force can change the shape of the body. 
5. Force can stop a moving object. 
 
Representation Of Force 
Force is a vector quantity having both direction and 
magnitude.  
S.I. unit of force is Newton (N).  
The direction of force can easily be represented by an arrow 
( ? ) pointing in the direction of force.  
 
Types Of Forces 
1. Normal Force 
2. Weight 
3. Friction 
 
Balanced And Unbalanced Forces 
 
Balanced Forces 
When equal amount of forces act on an object, the forces are 
said to be balanced. So balanced forces do not change the 
state of rest, motion or shape of the body. 
 
 
Unbalanced Forces 
Forces are said to be unbalanced when magnitude of one 
force applied on an object is greater than other. In this, state 
of the object changes in the direction of the resultant force. 
 
Resultant Force 
Resultant force is that single force acting on a body which 
produces the same effect or acceleration as produced by 
number of forces acting simultaneously. 
Newton’s Laws Of Motion 
Newton’s Laws of motion describe motion of body. These laws 
give us a definition of force.  They give a relationship between 
the force applied on a body and the state of motion acquired 
by it.  
 
1. Newton’s First Law of Motion 
A body at rest will continue to be at rest or a body in 
motion will remain in motion in same straight line with 
a uniform speed until or unless it is compelled by an 
external force to change its state of rest or of uniform 
motion.  Newton’s first law recognizes that every body has 
some inertia.   
 
Inertia 
Inertia is that property of a body due to which the body resists 
change in the state of its rest or of motion.  Inertia of a body 
is measured by measuring mass of the body.  If a body has 
more mass it has more inertia and vice versa. 
 
Example Of Inertia 
Make a pile of similar coins.  If we strike at the bottom of pile 
by another coin with our fingers fastly, we may find that only 
the coin at the bottom moves out of the pile. Rest of the pile 
remains intact because the inertia of rest of remaining coins 
prevents them from moving.    
 
Types Of Inertia 
1. Inertia of rest. 
2. Inertia of motion. 
3. Inertia of direction. 
 
Why It Is Advised To Tie Luggage With A  Rope On The 
Roof Of Buses?  
Because if the bus starts suddenly the luggage due to inertia 
of rest tends to remain in the state of rest and that is why 
some of the luggage might fall towards the backside of bus. 
Same as if the bus will stop suddenly the luggage due to 
inertia of motion remain in motion and might fall in the front if 
it is not tied with a rope.  
 
Why Some Space Is Left At The Top In Oil Tankers 
While Filling Them? 
Because if the moving oil tanker stops suddenly, the oil due to 
inertia of motion splashes and will overflow same as when 
tanker will move suddenly the oil will move backward and will 
overflow if no space is left.   
 
When A Running Car Or Bus Stops Suddenly Why 
Passengers Fall Forward? 
Due to their inertia of motion the passengers tend to remain in 
their state of motion and tend to move forward even though 
the car or bus has come to rest. That is why the passengers 
get a jerk and fall forward when a running car or bus stops 
suddenly. Same way they fall backward when the bus or car 
starts moving suddenly due to inertia of rest. 
 
Page 2


 
 
FORCE AND LAWS OF MOTION
A body at rest can be moved and one that is moving can be 
brought to rest. What makes bodies to move or change their 
direction of motion or stop, if they are moving?  We can say 
that it is a push or pull applied to the objects make them move 
or stop or change their shape.  The push or pull is actually the 
force applied in any way. Therefore we can define force as: –  
Force is an influence which tends to set a stationary 
body in motion or change the speed and direction of a 
moving body or change the shape of a body. Force is a 
vector quantity; it is having magnitude as well as 
direction. 
 
Effects Of Force 
1. Force can move a body at rest. 
2. Force can accelerate or decelerate a body. 
3. Force can change the direction of motion. 
4. Force can change the shape of the body. 
5. Force can stop a moving object. 
 
Representation Of Force 
Force is a vector quantity having both direction and 
magnitude.  
S.I. unit of force is Newton (N).  
The direction of force can easily be represented by an arrow 
( ? ) pointing in the direction of force.  
 
Types Of Forces 
1. Normal Force 
2. Weight 
3. Friction 
 
Balanced And Unbalanced Forces 
 
Balanced Forces 
When equal amount of forces act on an object, the forces are 
said to be balanced. So balanced forces do not change the 
state of rest, motion or shape of the body. 
 
 
Unbalanced Forces 
Forces are said to be unbalanced when magnitude of one 
force applied on an object is greater than other. In this, state 
of the object changes in the direction of the resultant force. 
 
Resultant Force 
Resultant force is that single force acting on a body which 
produces the same effect or acceleration as produced by 
number of forces acting simultaneously. 
Newton’s Laws Of Motion 
Newton’s Laws of motion describe motion of body. These laws 
give us a definition of force.  They give a relationship between 
the force applied on a body and the state of motion acquired 
by it.  
 
1. Newton’s First Law of Motion 
A body at rest will continue to be at rest or a body in 
motion will remain in motion in same straight line with 
a uniform speed until or unless it is compelled by an 
external force to change its state of rest or of uniform 
motion.  Newton’s first law recognizes that every body has 
some inertia.   
 
Inertia 
Inertia is that property of a body due to which the body resists 
change in the state of its rest or of motion.  Inertia of a body 
is measured by measuring mass of the body.  If a body has 
more mass it has more inertia and vice versa. 
 
Example Of Inertia 
Make a pile of similar coins.  If we strike at the bottom of pile 
by another coin with our fingers fastly, we may find that only 
the coin at the bottom moves out of the pile. Rest of the pile 
remains intact because the inertia of rest of remaining coins 
prevents them from moving.    
 
Types Of Inertia 
1. Inertia of rest. 
2. Inertia of motion. 
3. Inertia of direction. 
 
Why It Is Advised To Tie Luggage With A  Rope On The 
Roof Of Buses?  
Because if the bus starts suddenly the luggage due to inertia 
of rest tends to remain in the state of rest and that is why 
some of the luggage might fall towards the backside of bus. 
Same as if the bus will stop suddenly the luggage due to 
inertia of motion remain in motion and might fall in the front if 
it is not tied with a rope.  
 
Why Some Space Is Left At The Top In Oil Tankers 
While Filling Them? 
Because if the moving oil tanker stops suddenly, the oil due to 
inertia of motion splashes and will overflow same as when 
tanker will move suddenly the oil will move backward and will 
overflow if no space is left.   
 
When A Running Car Or Bus Stops Suddenly Why 
Passengers Fall Forward? 
Due to their inertia of motion the passengers tend to remain in 
their state of motion and tend to move forward even though 
the car or bus has come to rest. That is why the passengers 
get a jerk and fall forward when a running car or bus stops 
suddenly. Same way they fall backward when the bus or car 
starts moving suddenly due to inertia of rest. 
 
 
 
Why Can Dust Be Removed From A Carpet By Shaking, 
Or By Beating It With A Stick? 
Initially both the carpet and the dust therein are at rest. When 
the carpet is shaken, or beaten with a stick the carpet is set 
into motion. Due to the inertia of rest, the dust particles tend 
to remain at rest. As a result the dust particles fall off. 
 
Why Do Passengers Tend To Fall Sideways When The 
Bus Takes A Sharp Turn? 
When the bus runs along the straight line path, all the 
passengers traveling in the bus also move with the same 
speed in the same direction. When the bus takes a sharp turn, 
the upper body portion of the passengers still continue to 
move in the original straight line path, while the lower portion 
tend to turn with the bus. As a result passengers tend to fall 
sideways. 
 
Why The Passengers Fall Backward Or Forward When 
The Bus Or Train Starts Or Stops Respectively? 
It due to the effect of inertia the passengers continue to 
remain in their state of rest or of motion in the vehicle due to 
which they fall. 
 
 
 
 
 
2. Newton’s Second Law of Motion 
It states that the force is directly proportional to the 
product of its mass and acceleration and it always acts 
in the direction of force. It recognizes the law of 
momentum. 
 
Law Of Momentum 
It states that the rate of change of momentum of a body is 
directly proportional to force and it takes place in the same 
direction as the force.  
The concept of momentum is introduced in Newton’s second 
Law of Motion. 
 
Momentum 
Momentum of a moving body is defined as product of its mass 
and velocity. Momentum is a vector quantity. It has the same 
direction as the velocity of the body.  
 
p  =  mv  
Where   
p = momentum  
m = mass  
v = velocity 
 
According to the Newton’s second law of motion suppose the 
velocity of a body of mass m changes from u to v in time t.  
The sizes of the initial and final momentum will be p
1
 = mu 
and p
2 
 = mv respectively.  The change in the momentum (p
2
 
– p
1
) takes place in time t.  Now the magnitude of the force f, 
is  
t
p p
F
1 2
-
?   
m(v u)
F
t
-
?= 
or 
m(v u)
F K
t
-
=                             …………………….(i) 
 
Where k =  constant of proportionality   
 
Now,
t
u) (v -
 is the equal to rate of change of velocity i.e., 
acceleration ‘a’ so by putting the value in (i) we get, 
 
F  =  kma 
The value in S.I. units of k = 1, so by putting this value of k in 
the above formula we get, 
 
F = ma 
 
Now, we can state that force is the product of mass and 
acceleration of a body. 
 
Units Of Force 
F =  kg  x  ms
2
   ? kg m/s
2      
? N
 
 
This unit of force has a special name Newton and it is 
denoted by symbol ‘N’ with the Newton’s second law we can 
measure force, when mass of a body and its acceleration due 
to a force are known. 
 
3. Newton’s Third Law Of Motion 
It states that whenever one body exerts a force on 
another body, the second body exerts equal and 
opposite force on first body.    
Or     
To every action there is an equal and opposite reaction. 
 
Action and reaction act on two different bodies but they act 
simultaneously. Newton’s third law tells us that at least two 
bodies are necessary for a force to exist.  For example, if we 
hit a table with our palm we apply force.  The table also exerts 
an equal and opposite force on our palm as we hit it.  The 
pain experience by us in our palm is due to this force or 
 
Page 3


 
 
FORCE AND LAWS OF MOTION
A body at rest can be moved and one that is moving can be 
brought to rest. What makes bodies to move or change their 
direction of motion or stop, if they are moving?  We can say 
that it is a push or pull applied to the objects make them move 
or stop or change their shape.  The push or pull is actually the 
force applied in any way. Therefore we can define force as: –  
Force is an influence which tends to set a stationary 
body in motion or change the speed and direction of a 
moving body or change the shape of a body. Force is a 
vector quantity; it is having magnitude as well as 
direction. 
 
Effects Of Force 
1. Force can move a body at rest. 
2. Force can accelerate or decelerate a body. 
3. Force can change the direction of motion. 
4. Force can change the shape of the body. 
5. Force can stop a moving object. 
 
Representation Of Force 
Force is a vector quantity having both direction and 
magnitude.  
S.I. unit of force is Newton (N).  
The direction of force can easily be represented by an arrow 
( ? ) pointing in the direction of force.  
 
Types Of Forces 
1. Normal Force 
2. Weight 
3. Friction 
 
Balanced And Unbalanced Forces 
 
Balanced Forces 
When equal amount of forces act on an object, the forces are 
said to be balanced. So balanced forces do not change the 
state of rest, motion or shape of the body. 
 
 
Unbalanced Forces 
Forces are said to be unbalanced when magnitude of one 
force applied on an object is greater than other. In this, state 
of the object changes in the direction of the resultant force. 
 
Resultant Force 
Resultant force is that single force acting on a body which 
produces the same effect or acceleration as produced by 
number of forces acting simultaneously. 
Newton’s Laws Of Motion 
Newton’s Laws of motion describe motion of body. These laws 
give us a definition of force.  They give a relationship between 
the force applied on a body and the state of motion acquired 
by it.  
 
1. Newton’s First Law of Motion 
A body at rest will continue to be at rest or a body in 
motion will remain in motion in same straight line with 
a uniform speed until or unless it is compelled by an 
external force to change its state of rest or of uniform 
motion.  Newton’s first law recognizes that every body has 
some inertia.   
 
Inertia 
Inertia is that property of a body due to which the body resists 
change in the state of its rest or of motion.  Inertia of a body 
is measured by measuring mass of the body.  If a body has 
more mass it has more inertia and vice versa. 
 
Example Of Inertia 
Make a pile of similar coins.  If we strike at the bottom of pile 
by another coin with our fingers fastly, we may find that only 
the coin at the bottom moves out of the pile. Rest of the pile 
remains intact because the inertia of rest of remaining coins 
prevents them from moving.    
 
Types Of Inertia 
1. Inertia of rest. 
2. Inertia of motion. 
3. Inertia of direction. 
 
Why It Is Advised To Tie Luggage With A  Rope On The 
Roof Of Buses?  
Because if the bus starts suddenly the luggage due to inertia 
of rest tends to remain in the state of rest and that is why 
some of the luggage might fall towards the backside of bus. 
Same as if the bus will stop suddenly the luggage due to 
inertia of motion remain in motion and might fall in the front if 
it is not tied with a rope.  
 
Why Some Space Is Left At The Top In Oil Tankers 
While Filling Them? 
Because if the moving oil tanker stops suddenly, the oil due to 
inertia of motion splashes and will overflow same as when 
tanker will move suddenly the oil will move backward and will 
overflow if no space is left.   
 
When A Running Car Or Bus Stops Suddenly Why 
Passengers Fall Forward? 
Due to their inertia of motion the passengers tend to remain in 
their state of motion and tend to move forward even though 
the car or bus has come to rest. That is why the passengers 
get a jerk and fall forward when a running car or bus stops 
suddenly. Same way they fall backward when the bus or car 
starts moving suddenly due to inertia of rest. 
 
 
 
Why Can Dust Be Removed From A Carpet By Shaking, 
Or By Beating It With A Stick? 
Initially both the carpet and the dust therein are at rest. When 
the carpet is shaken, or beaten with a stick the carpet is set 
into motion. Due to the inertia of rest, the dust particles tend 
to remain at rest. As a result the dust particles fall off. 
 
Why Do Passengers Tend To Fall Sideways When The 
Bus Takes A Sharp Turn? 
When the bus runs along the straight line path, all the 
passengers traveling in the bus also move with the same 
speed in the same direction. When the bus takes a sharp turn, 
the upper body portion of the passengers still continue to 
move in the original straight line path, while the lower portion 
tend to turn with the bus. As a result passengers tend to fall 
sideways. 
 
Why The Passengers Fall Backward Or Forward When 
The Bus Or Train Starts Or Stops Respectively? 
It due to the effect of inertia the passengers continue to 
remain in their state of rest or of motion in the vehicle due to 
which they fall. 
 
 
 
 
 
2. Newton’s Second Law of Motion 
It states that the force is directly proportional to the 
product of its mass and acceleration and it always acts 
in the direction of force. It recognizes the law of 
momentum. 
 
Law Of Momentum 
It states that the rate of change of momentum of a body is 
directly proportional to force and it takes place in the same 
direction as the force.  
The concept of momentum is introduced in Newton’s second 
Law of Motion. 
 
Momentum 
Momentum of a moving body is defined as product of its mass 
and velocity. Momentum is a vector quantity. It has the same 
direction as the velocity of the body.  
 
p  =  mv  
Where   
p = momentum  
m = mass  
v = velocity 
 
According to the Newton’s second law of motion suppose the 
velocity of a body of mass m changes from u to v in time t.  
The sizes of the initial and final momentum will be p
1
 = mu 
and p
2 
 = mv respectively.  The change in the momentum (p
2
 
– p
1
) takes place in time t.  Now the magnitude of the force f, 
is  
t
p p
F
1 2
-
?   
m(v u)
F
t
-
?= 
or 
m(v u)
F K
t
-
=                             …………………….(i) 
 
Where k =  constant of proportionality   
 
Now,
t
u) (v -
 is the equal to rate of change of velocity i.e., 
acceleration ‘a’ so by putting the value in (i) we get, 
 
F  =  kma 
The value in S.I. units of k = 1, so by putting this value of k in 
the above formula we get, 
 
F = ma 
 
Now, we can state that force is the product of mass and 
acceleration of a body. 
 
Units Of Force 
F =  kg  x  ms
2
   ? kg m/s
2      
? N
 
 
This unit of force has a special name Newton and it is 
denoted by symbol ‘N’ with the Newton’s second law we can 
measure force, when mass of a body and its acceleration due 
to a force are known. 
 
3. Newton’s Third Law Of Motion 
It states that whenever one body exerts a force on 
another body, the second body exerts equal and 
opposite force on first body.    
Or     
To every action there is an equal and opposite reaction. 
 
Action and reaction act on two different bodies but they act 
simultaneously. Newton’s third law tells us that at least two 
bodies are necessary for a force to exist.  For example, if we 
hit a table with our palm we apply force.  The table also exerts 
an equal and opposite force on our palm as we hit it.  The 
pain experience by us in our palm is due to this force or 
 
 
reaction of the table.  It tells us that the forces always occur in 
pairs.  It is not possible to obtain a single force. 
 
Law Of Conservation Of Momentum 
It states that when two or more bodies act upon one 
another, their total momentum remains constant (or 
conserved) provided there is no external force acting 
on them. It means that whenever one body looses 
momentum, then some other body must gain an equal amount 
of momentum, but the total momentum remains conserved.  
For example, consider two marbles A and B having masses m
1
 
and m
2
 respectively 
 
Let, 
Initial velocity of marble A = u
1
 
Initial velocity of marble B = u
2
 
 
Suppose the two marbles collide head on with each other and 
the collision occurs for t seconds.  After the collision suppose 
the velocities of marbles become 
 
Final velocity of marble A = v
1
,  
Final velocity of marble B = v
2
 
Momentum before collision of marble A =  m
1
 u
1
 
Momentum after collision of marble    A  = m
1
 v
1
 
Now, 
Rate of change of momentum for marble A 
                       = 
t
) u (v m
1 1 1
-
  =  
t
v m u m
1 1 1 1
-
 
 
Similarly, for marble B 
Rate of change of momentum for marble B 
= 
t
u (v m
2 2 2
) -
 = 
t
v m u m
2 2 2 2
-
 
 
If force exerted by marble A on B is F
A
 and that by B on A is 
F
B
 then according to the second law of motion 
F
A
 = 
t
) u (v m
1 1 1
-
 and  F
B
 = 
t
) u (v m
2 2 2
-
    
 
 
According to the third law of motion F
A
 = – F
B
 due to the 
exertion of equal and opposite forces on each of the marbles. 
By substituting values  
 
t
) u (v m
t
) u (v m
2 2 2 1 1 1
-
- =
-
 
 
? 
t
u m v m
t
u m v m
2 2 2 2 1 1 1 1
+
- =
-
 
 
? 
t
u m
t
v m
t
u m
t
v m
2 2 2 2 1 1 1 1
+ - = - 
 
? 
t
u m
t
v m
t
v m
t
v m
2 2 1 1 2 2 1 1
+ = + 
 
? 
t
v m
t
v m
t
u m
t
u m
2 2 1 1 2 2 1 1
+ = + 
 
Canceling t from both sides, we get   
 
          m
1
u
1
 + m
2
 u
2
         =              m
1
v
1
 + m
2
 v
2
   
(Momentum Before Collision)        (Momentum After Collision)                                                    
 
Thus, in collision between two marbles the total momentum 
before and after the collision remains unchanged or conserved 
provided no other forces are acting upon them. 
 
Why Does A Boat Move Backwards Into Water When A 
Person Jumps Out Of It Onto The Bank Of The River? 
To jump out of a boat, a person requires a certain momentum. 
To gain the required momentum the person applies force in 
the forward direction. The reaction of this force acts on the 
boat and in the opposite direction. As a result when the person 
moves in the forward direction the boat moves in the 
backward direction.  
 
How Do Jet Aeroplanes And Rockets Work? 
In jet engines and rockets, the fuel burnt to produce a large 
quantity of hot gases. These hot gases come out of a nozzle 
with a great force. These out coming gases with such gas 
exert an equal and opposite force on the rocket. Thus, the jet 
aeroplanes move forward due to the reaction exerted by the 
out coming gases. 
                      
Friction   
Friction is the force which always opposes the motion of one 
body over another body in contact with. The force of friction is 
always opposite to the direction of motion of the body. 
 
Cause Of Friction 
Friction is caused due to the roughness of surfaces. The more 
is the surface rough, the more is the friction. 
 
Types Of Friction 
1. Static Friction (Limiting Friction) 
2. Dynamic Friction (Sliding For Kinetic Friction) 
3. Rolling Friction 
 
1. Static Or Limiting Friction 
It is the friction between any two bodies when one of the 
bodies just tends to move or slip over the surface of another 
body. In static friction there is no actual movement of the 
body.  For example if we keep a wooden block on a tabletop. 
Push or pull the block by applying small force. Brick may not 
move at all because its motion is opposed by the force of 
 
Page 4


 
 
FORCE AND LAWS OF MOTION
A body at rest can be moved and one that is moving can be 
brought to rest. What makes bodies to move or change their 
direction of motion or stop, if they are moving?  We can say 
that it is a push or pull applied to the objects make them move 
or stop or change their shape.  The push or pull is actually the 
force applied in any way. Therefore we can define force as: –  
Force is an influence which tends to set a stationary 
body in motion or change the speed and direction of a 
moving body or change the shape of a body. Force is a 
vector quantity; it is having magnitude as well as 
direction. 
 
Effects Of Force 
1. Force can move a body at rest. 
2. Force can accelerate or decelerate a body. 
3. Force can change the direction of motion. 
4. Force can change the shape of the body. 
5. Force can stop a moving object. 
 
Representation Of Force 
Force is a vector quantity having both direction and 
magnitude.  
S.I. unit of force is Newton (N).  
The direction of force can easily be represented by an arrow 
( ? ) pointing in the direction of force.  
 
Types Of Forces 
1. Normal Force 
2. Weight 
3. Friction 
 
Balanced And Unbalanced Forces 
 
Balanced Forces 
When equal amount of forces act on an object, the forces are 
said to be balanced. So balanced forces do not change the 
state of rest, motion or shape of the body. 
 
 
Unbalanced Forces 
Forces are said to be unbalanced when magnitude of one 
force applied on an object is greater than other. In this, state 
of the object changes in the direction of the resultant force. 
 
Resultant Force 
Resultant force is that single force acting on a body which 
produces the same effect or acceleration as produced by 
number of forces acting simultaneously. 
Newton’s Laws Of Motion 
Newton’s Laws of motion describe motion of body. These laws 
give us a definition of force.  They give a relationship between 
the force applied on a body and the state of motion acquired 
by it.  
 
1. Newton’s First Law of Motion 
A body at rest will continue to be at rest or a body in 
motion will remain in motion in same straight line with 
a uniform speed until or unless it is compelled by an 
external force to change its state of rest or of uniform 
motion.  Newton’s first law recognizes that every body has 
some inertia.   
 
Inertia 
Inertia is that property of a body due to which the body resists 
change in the state of its rest or of motion.  Inertia of a body 
is measured by measuring mass of the body.  If a body has 
more mass it has more inertia and vice versa. 
 
Example Of Inertia 
Make a pile of similar coins.  If we strike at the bottom of pile 
by another coin with our fingers fastly, we may find that only 
the coin at the bottom moves out of the pile. Rest of the pile 
remains intact because the inertia of rest of remaining coins 
prevents them from moving.    
 
Types Of Inertia 
1. Inertia of rest. 
2. Inertia of motion. 
3. Inertia of direction. 
 
Why It Is Advised To Tie Luggage With A  Rope On The 
Roof Of Buses?  
Because if the bus starts suddenly the luggage due to inertia 
of rest tends to remain in the state of rest and that is why 
some of the luggage might fall towards the backside of bus. 
Same as if the bus will stop suddenly the luggage due to 
inertia of motion remain in motion and might fall in the front if 
it is not tied with a rope.  
 
Why Some Space Is Left At The Top In Oil Tankers 
While Filling Them? 
Because if the moving oil tanker stops suddenly, the oil due to 
inertia of motion splashes and will overflow same as when 
tanker will move suddenly the oil will move backward and will 
overflow if no space is left.   
 
When A Running Car Or Bus Stops Suddenly Why 
Passengers Fall Forward? 
Due to their inertia of motion the passengers tend to remain in 
their state of motion and tend to move forward even though 
the car or bus has come to rest. That is why the passengers 
get a jerk and fall forward when a running car or bus stops 
suddenly. Same way they fall backward when the bus or car 
starts moving suddenly due to inertia of rest. 
 
 
 
Why Can Dust Be Removed From A Carpet By Shaking, 
Or By Beating It With A Stick? 
Initially both the carpet and the dust therein are at rest. When 
the carpet is shaken, or beaten with a stick the carpet is set 
into motion. Due to the inertia of rest, the dust particles tend 
to remain at rest. As a result the dust particles fall off. 
 
Why Do Passengers Tend To Fall Sideways When The 
Bus Takes A Sharp Turn? 
When the bus runs along the straight line path, all the 
passengers traveling in the bus also move with the same 
speed in the same direction. When the bus takes a sharp turn, 
the upper body portion of the passengers still continue to 
move in the original straight line path, while the lower portion 
tend to turn with the bus. As a result passengers tend to fall 
sideways. 
 
Why The Passengers Fall Backward Or Forward When 
The Bus Or Train Starts Or Stops Respectively? 
It due to the effect of inertia the passengers continue to 
remain in their state of rest or of motion in the vehicle due to 
which they fall. 
 
 
 
 
 
2. Newton’s Second Law of Motion 
It states that the force is directly proportional to the 
product of its mass and acceleration and it always acts 
in the direction of force. It recognizes the law of 
momentum. 
 
Law Of Momentum 
It states that the rate of change of momentum of a body is 
directly proportional to force and it takes place in the same 
direction as the force.  
The concept of momentum is introduced in Newton’s second 
Law of Motion. 
 
Momentum 
Momentum of a moving body is defined as product of its mass 
and velocity. Momentum is a vector quantity. It has the same 
direction as the velocity of the body.  
 
p  =  mv  
Where   
p = momentum  
m = mass  
v = velocity 
 
According to the Newton’s second law of motion suppose the 
velocity of a body of mass m changes from u to v in time t.  
The sizes of the initial and final momentum will be p
1
 = mu 
and p
2 
 = mv respectively.  The change in the momentum (p
2
 
– p
1
) takes place in time t.  Now the magnitude of the force f, 
is  
t
p p
F
1 2
-
?   
m(v u)
F
t
-
?= 
or 
m(v u)
F K
t
-
=                             …………………….(i) 
 
Where k =  constant of proportionality   
 
Now,
t
u) (v -
 is the equal to rate of change of velocity i.e., 
acceleration ‘a’ so by putting the value in (i) we get, 
 
F  =  kma 
The value in S.I. units of k = 1, so by putting this value of k in 
the above formula we get, 
 
F = ma 
 
Now, we can state that force is the product of mass and 
acceleration of a body. 
 
Units Of Force 
F =  kg  x  ms
2
   ? kg m/s
2      
? N
 
 
This unit of force has a special name Newton and it is 
denoted by symbol ‘N’ with the Newton’s second law we can 
measure force, when mass of a body and its acceleration due 
to a force are known. 
 
3. Newton’s Third Law Of Motion 
It states that whenever one body exerts a force on 
another body, the second body exerts equal and 
opposite force on first body.    
Or     
To every action there is an equal and opposite reaction. 
 
Action and reaction act on two different bodies but they act 
simultaneously. Newton’s third law tells us that at least two 
bodies are necessary for a force to exist.  For example, if we 
hit a table with our palm we apply force.  The table also exerts 
an equal and opposite force on our palm as we hit it.  The 
pain experience by us in our palm is due to this force or 
 
 
reaction of the table.  It tells us that the forces always occur in 
pairs.  It is not possible to obtain a single force. 
 
Law Of Conservation Of Momentum 
It states that when two or more bodies act upon one 
another, their total momentum remains constant (or 
conserved) provided there is no external force acting 
on them. It means that whenever one body looses 
momentum, then some other body must gain an equal amount 
of momentum, but the total momentum remains conserved.  
For example, consider two marbles A and B having masses m
1
 
and m
2
 respectively 
 
Let, 
Initial velocity of marble A = u
1
 
Initial velocity of marble B = u
2
 
 
Suppose the two marbles collide head on with each other and 
the collision occurs for t seconds.  After the collision suppose 
the velocities of marbles become 
 
Final velocity of marble A = v
1
,  
Final velocity of marble B = v
2
 
Momentum before collision of marble A =  m
1
 u
1
 
Momentum after collision of marble    A  = m
1
 v
1
 
Now, 
Rate of change of momentum for marble A 
                       = 
t
) u (v m
1 1 1
-
  =  
t
v m u m
1 1 1 1
-
 
 
Similarly, for marble B 
Rate of change of momentum for marble B 
= 
t
u (v m
2 2 2
) -
 = 
t
v m u m
2 2 2 2
-
 
 
If force exerted by marble A on B is F
A
 and that by B on A is 
F
B
 then according to the second law of motion 
F
A
 = 
t
) u (v m
1 1 1
-
 and  F
B
 = 
t
) u (v m
2 2 2
-
    
 
 
According to the third law of motion F
A
 = – F
B
 due to the 
exertion of equal and opposite forces on each of the marbles. 
By substituting values  
 
t
) u (v m
t
) u (v m
2 2 2 1 1 1
-
- =
-
 
 
? 
t
u m v m
t
u m v m
2 2 2 2 1 1 1 1
+
- =
-
 
 
? 
t
u m
t
v m
t
u m
t
v m
2 2 2 2 1 1 1 1
+ - = - 
 
? 
t
u m
t
v m
t
v m
t
v m
2 2 1 1 2 2 1 1
+ = + 
 
? 
t
v m
t
v m
t
u m
t
u m
2 2 1 1 2 2 1 1
+ = + 
 
Canceling t from both sides, we get   
 
          m
1
u
1
 + m
2
 u
2
         =              m
1
v
1
 + m
2
 v
2
   
(Momentum Before Collision)        (Momentum After Collision)                                                    
 
Thus, in collision between two marbles the total momentum 
before and after the collision remains unchanged or conserved 
provided no other forces are acting upon them. 
 
Why Does A Boat Move Backwards Into Water When A 
Person Jumps Out Of It Onto The Bank Of The River? 
To jump out of a boat, a person requires a certain momentum. 
To gain the required momentum the person applies force in 
the forward direction. The reaction of this force acts on the 
boat and in the opposite direction. As a result when the person 
moves in the forward direction the boat moves in the 
backward direction.  
 
How Do Jet Aeroplanes And Rockets Work? 
In jet engines and rockets, the fuel burnt to produce a large 
quantity of hot gases. These hot gases come out of a nozzle 
with a great force. These out coming gases with such gas 
exert an equal and opposite force on the rocket. Thus, the jet 
aeroplanes move forward due to the reaction exerted by the 
out coming gases. 
                      
Friction   
Friction is the force which always opposes the motion of one 
body over another body in contact with. The force of friction is 
always opposite to the direction of motion of the body. 
 
Cause Of Friction 
Friction is caused due to the roughness of surfaces. The more 
is the surface rough, the more is the friction. 
 
Types Of Friction 
1. Static Friction (Limiting Friction) 
2. Dynamic Friction (Sliding For Kinetic Friction) 
3. Rolling Friction 
 
1. Static Or Limiting Friction 
It is the friction between any two bodies when one of the 
bodies just tends to move or slip over the surface of another 
body. In static friction there is no actual movement of the 
body.  For example if we keep a wooden block on a tabletop. 
Push or pull the block by applying small force. Brick may not 
move at all because its motion is opposed by the force of 
 
 
friction which cuts in the opposite direction. As we increased 
the applied force, the force of friction also goes on increasing. 
Ultimately when the applied force is becomes a little more 
than the maximum frictional force, and then wooden block 
tends to move. This means that the frictional force has a 
maximum value beyond which it cannot increase. So we can 
say that the maximum frictional force present when a body 
just tends to slip over the surface of another body is called 
static friction or limiting friction. 
 
2. Dynamic Or Sliding Friction 
The frictional force present when a body moves slowly or 
slides over another body is known as sliding or dynamic 
friction. For example if we keep a wooden block on a table top 
then the force required to keep the block sliding, once it has 
started sliding is less than the static or limiting friction. In 
other words, when a body started sliding, the friction is less. 
So, we can say that static friction is more than dynamic 
friction. 
 
3. Rolling Friction 
When a body like a roller or wheel rolls over the surface of 
another body, the friction is called rolling friction. 
 
The rolling friction is due to two reasons:- 
(i) The rolling body deforms the surface a little bit on which 
is rolls, 
(ii) The rolling body itself gets deformed at its point of 
contact with the surface. 
 
Rolling friction is much less than sliding friction therefore it is 
heavier to roll a heavy drum than to drag it. 
 
Friction Exerted By Liquids And Gases 
Friction exerted by liquids and gases is much less as compared 
to solids. Friction due to air is weakest. To lessen or minimize 
the friction exerted by liquids and gases, the objects which 
made to move in it are streamlined. (Streamlined shape is the 
shape of the body or object around which a fluid can flow past 
easily.) For example, the shape of boat, ship and aeroplane 
are made streamlined to face less resistance due to air and 
water. Even the shape of fish and birds are naturally 
streamlined. 
 
Example Of Friction Exerted By Water  
When a person swims in water, the water opposes his motion. 
Due to which the swimmer has to apply force to pass through 
water. 
 
Example Of Friction Exerted By Air 
When the meteors fall through the earth’s atmosphere the 
friction of air opposes their motion. Due to the very high speed 
of meteors through air, the air produces a very large heat and 
the meteors start burning. They burn up completely before 
reaching to the earth. Only a few large meteors burn partially 
and reach surface of earth and are called meteorites. 
 
Usefulness Of Friction 
1. It makes us able to walk and prevent slipping. 
2. With the help of friction belts can drive machines. 
3. Brakes of cars and other vehicles can be applied with the 
help of friction. 
4. Knots can be tied. 
5. Nails and screws can be used to hold things together. 
6. Friction enables us to write on paper. 
7. Lighting of a matchstick is due to friction in both surfaces. 
8. Due to greater friction the tyres get a better grip on the 
road which prevents skidding of the vehicle. 
9. Spikes are provided in the shoes of players and athletes to 
increase friction and prevent slipping. 
 
Harmfulness Of Friction 
1. Reduces the efficiency of machines. 
2. Friction produces heat which could damage the machine. 
3. Friction wears out the rubbing machine parts gradually. 
 
Methods Of Reducing Friction 
1. By polishing or applying lubricants to surfaces. 
2. By using ball bearings. 
3. By using rollers and wheels. 
4. By streamlining the shape of the object.