Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. It can be expressed by the equation: F=ma, where F is the net force, m is the mass of the object, and a is the acceleration. A force of 1 Newton is defined as the force required to accelerate 1 kilogram of mass at a rate of 1 meter per second squared. Newton's third law states that for every action force there is an equal and opposite reaction force. The principle of conservation of momentum states that the total momentum of a system remains constant if no external force acts on the system.

1. Newton’s First Law
In the absence of external forces and an object at rest remains at rest and an object
in motion continues in motion with a constant velocity.
In other words, when no force acts on an object, the acceleration of the object
is zero. From the first law, it can be concluded that any isolated object (one
that does not interact with its environment) is either at rest or moving with
constant velocity. The tendency of an object to resist any attempt to change its
velocity is called inertia.
Mass and Inertia
The tendency of an object to continue in its original state of motion is called inertia.
While inertia is the tendency of an object to continue its motion in the absence of a force,
mass is a measure of the object’s resistance to changes in its motion due to a force. The
greater the mass of a body, the less it accelerates under the action of a given applied force.
The SI unit of mass is the kilogram. Mass is a scalar quantity
that obeys the rules of ordinary arithmetic.
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2. NEWTON’S SECOND LAW
If we Imagine a block of ice of mass m is pushed across a frictionless horizontal
surface. When some horizontal force is exerted on the block, it moves with an
acceleration of, say .If force is applied, as large , the acceleration
doubles to . Pushing three times as hard triples the acceleration, and so on.
From such observations, we conclude that the acceleration of an object is directly
proportional to the net force acting on it i.e.
F
ur
2
2
m
a
s

r
2F
ur
2
4
m
a
s

r
F a
ur r
Mass also affects the acceleration. Suppose we stack identical blocks of ice on top of each
other while pushing the stack with constant force. If the force applied to one block of
mass m produces an acceleration , when two blocks are pushed by the same force
then the acceleration drops to half . when three blocks are pushed the acceleration
is It can be conclude that the acceleration of an object is inversely proportional
to its mass.
F
ur
2
2
m
a
s

r
F
ur
2
1
m
a
s

r
2
1
3
m
a
s

r
1
a 
r
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3. The acceleration of an object is directly proportional to the net force
acting on it and inversely proportional to its mass.
The constant of proportionality is equal to one, so in mathematical
terms the preceding statement can be written
F
a
m


ur
r
Where is the acceleration of the object, m is its mass, and is the vector
sum of all forces acting on it.
a
r
F
ur
F ma
ur r
Statement of Newton’s second law
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4. But the acceleration,
v u
a
t


We can write rate of change of momentum = ma
From Newton’s second law F ma
F kma

 
Where k is a proportionality constant. When m= 1 unit, a
= 1 unit, then F = 1 unit. So we get
F k
The amount of force acts on an object with unit mass and
creates unit acceleration is called unit force.
1
1.1.1


k
k
So finally we get

5. One Newton force can be defined as the amount of force applied
to an object having a mass of 1 kg produces an acceleration of 1
m/s2 . Its unit is kgms-2
2 2
1 1 / 1
F ma
kg m s kgms

  
Definition of one Newton force
To every action there is an equal and opposite reaction
Newton’s 3rd law of motion

6. Units of Force and Mass
The SI unit of force is Newton. When 1 newton of force acts on an object that
has a mass of 1 kg, it produces an acceleration of 1 m/s2 in the object.
2
1 1 .
m
N kg
s

From this definition and Newton’s second law, the 1 Newton force can be
expressed in terms of the fundamental units of mass, length, and time as
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7. Newton’s Third Law
If body A exerts a force on body B (an “action”), then body B exerts a force
on body A (a “reaction”). These two forces have the same magnitude but
are opposite in direction. These two forces act on different bodies.
AonBF
ur
For example, in Fig. 4.25 is the force
applied by body A on body B. is the force
applied by body B on body A. The
mathematical statement of
Newton’s third law is
BonAF
ur
F
ur
A on B
= F
ur
B on A
AonBF
ur
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8. Impulse and momentum
Impulsive force
Impulsive force is a force of very high magnitude which acts for a very short time.
Impulse
The product of the impulsive force and the time during which the
force acts is called impulse. It is denoted by J , it is a vector quantity.
Explanation
Lets a strong force F acts on an object for very short time t. then
according to definition of impulse
J Ft mat 
ur ur r
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9. Momentum
The product of mass and velocity is called momentum. It is denoted by p
Explanation
If the mass of a body m and its velocity is v, so the momentum
p mv
Since v is a vector quantity, p also a vector quantity.
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10. Relation between impulse and momentum
We know
J Ft mat 
ur ur r
If is the initial velocity and is the final velocity then we get,
0v
uur
fv
uur
 
0
0
0
f
f
f
v v
J m t
t
m v v
J mv mv
 
   
 
 
 
uur uur
ur
ur
Impulse = change of momentum 10

11. Principle of conservation of momentum
Principle
If no external forces act on a system of colliding objects, the total
momentum of the objects in a given direction before collision is
equal to the total momentum in the same direction after collision.
m1
u1
m2
u2
F1 F2
m1
v1
m1
v2
Before collision At the time of collision After collision
Let two objects of mass m1 and m2 move in the same direction in
straight line with velocity u1 and u2 respectively.
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Explanation:

12. At one time the first particle hits the second particle from behind and then the two particles
continue moving in the same direction and along the same line with velocities
and respectively.1v 2v
Let the time of action and reaction due to collision be t, thus the resultant of initial
momentum of the two particles
1 1 2 2m u m u
The resultant of the final momentum of the particles
1 1 2 2m v m v
According to the principle of conservation of momentum
1 1 2 2 1 1 2 2m u m u m v m v  
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13. Rate of change of momentum of the first particle =
1 1 1 1m v m u
t

ur ur
Rate of change of momentum of the second particles = 2 2 2 2m v m u
t

uur uur
= Reaction force = reaction force of the second particle on the first particle.
1F
uur
= action force =
2F
uur
= Applied force of the first particle on the second particle.
But the rate of change of momentum of the two particles (i.e. action force and
reaction force) are equal and opposite.
2 1F F 
uur uur
13
proof

14. 2 2 2 2 1 1 1 1
1 1 2 2 1 1 2 2
m v m u m v m u
t t
m u m u m v m v
 
 
   
uur uur ur ur
ur uur ur uur
So
Summation or resultant of the initial momentum of the two particles = summation or
resultant of the final momentum of the particles.
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