Short Notes of First year Physics Sindh Text Book Board

1. 1
Chapter no # 01
The scope of physics
Physics:
Physics the branch of science which deals the study of interaction of matter and
energy.
Branches of physics:
1) Mechanics:
The study about the stationary and moving objects.
2) Electrostatics:
The study about stationary charges.
3) Electrodynamics:
The study about moving charges. Or study about electricity.
4) Electromagnetism:
The study about behavior of magnets. Or the unification of stationary and
moving charges.
5) Optics:
The study about vision.
6) Nuclear physics:
The study about nucleus.
7) Atomic physics:
The study about atoms.
8) Geo physics:
The study about earth.
9) Astro physics:
The study about heavenly bodies.
10) Thermodynamics:
The study about conversion of heat in other form of energy and vice versa.
Fundamental quantities:
Quantity: anything which can be measured is called quantity.
The basic fundamental units are;
Length L Meter m
Mass M Kilogram Kg
Time t Second S
Luminous Intensity I Candela Cd
Temperature T Kelvin K
Amount of sub n mole mol
Electric current I Ampere A
System of Units:
Length Mass Time
M K S In S.I System

2. 2
C G S
F P S In B.E System
1 m = 100 cm
1 cm = 10 mm
1 m = 1000 mm
1 Km = 1000 m
1 Kg = 1000 g
1 m = 2.5 inch
Derived Units:
S.I CGS FPS
Speed V=S/t m/s cm/s ft/s
Acceleration a = Δv/t m/s2
cm/s2
ft/s2
Force F = ma Kgm/s2
gcm/s2
slug ft/s2
(Newton) (dyne) (Pound=Ib)
Work W = FS Nm = J dyne cm = Erg Ib ft =
B.T.U
Power P = w/t J/s = watt Erg/s B.T.U/s
Momentum = mV Kgm/s = N.S gcm/s Slug ft/s
 1 N = 105
dyne
1 N = 1 Kg X 1 m/s2
1 N = 1000 g X 100 cm/s2
1 N = 105
g cm/s5
1 N = 105
dyne
1 dyne = 10-5
N

3. 3
Chapter No 02
Scalars And Vectors
 Scalars and Vectors
 Scalars: The physical quantity which can be completely understood by magnitude
with poper unit.
Example: Heat, mass, density, speed, volume, Temperature, calorie, specific heat, energy,
distance, entropy, work, Gravitational, potential, charge, frequency, K.E ect.
 Vectors: The physical quantity which can be completely understood by showing
magnitude with proper unit and particular direction.
Example: Displacement, velocity, acceleration, power, force, momentum, angular
momentum, weight, magnetic field, intensity, centrifugal force, electric field intensity etc.
 Representation of vector
Length represents magnitude.
Arrow represents direction.
Length magnitude.
Tail Head
Vertical Horizontal
 Rules:-

4. 4
+ Y
180˚ 90˚
- X + X
270˚ 360˚
Origin Point
- Y
1) If x = +, y = +, Direction same as ɵ ( first quadrant ).
2) If X = - , y = +, Direction will be 180˚ - ɵ ( second quadrant ).
X = - , y = - , Direction will be 270˚ - ɵ or 180˚ + ɵ ( third quadrant ).
3) X = + , y = - , Direction will be 360˚ - ɵ ( fourth quadrant ).
N
+ y
W E
- x + x
- y
S
+ X , - X = 180˚
+ X , - Y = 90˚
+ X , - Y = 270˚
1) If two vectors are parallel o in same direction.
ɵ = 0˚
A
A B
B OR
2) If two vectors are perpendicular

5. 5
ɵ = 90˚ A
B
3) If two vectors are opposite or anti-parallel
ɵ = 180˚
A B A
B or
 Multiplication of Vector by a
Number
When +ve no: is multiplied with the vector then its magnitude increase in the direction.
Suppose:
A = 6 cm A = 6 cm
N = 2
n A = B B = 12 cm
2 X 6 = 12 Same direction
When -ve no: is multiplied with the vector then its magnitude increase in the opposite direction.
Suppose:
A = 6 cm A = 6 cm
N = - 2
n A = C C = - 12
-2 X 6 = - 12 opposite direction
 Division of a Vector by a Number
When +ve no: divided with the vector then its magnitude decrease in the same direction.
Suppose : A = 6 cm , n = 2
A = B

6. 6
n
6 = 3 cm 3 cm
2 Same direction
When - ve no is divide with the vector then its magnitude decreases in the opposite direction.
Suppose : A = 6 cm , n = - 2
A = B
n
6 = -3 B = - 3 cm
-2 opposite direction
 Vector Addition
Two or more than two vectors can be added by head to tail rule.
R B
A
A = direction
| A | = magnitude
| A | = unit vector
The magnitude of resultant vector is measured by cosine law.
| R | =√ A2
+ B2
+ 2AB cos ɵ
The direction of resultant vector is calculated by sine law.
1. If two vectors are Parallel (‖ ) , ɵ = 0˚.
A = 4 cm , B = 3 cm
= 4 + 3 = 7 cm

7. 7
Same direction
 The magnitude of resultant is “simple addition”.
 The direction of resultant is same as that of given vector.
2. If two vectors are perpendicular ( ḻ ) , θ = 90˚
B = 3
90˚
A = 4
 The magnitude of resultant is by “ Pathagorous Theorem ”.
| R | = √A2
+ B2
3. If two vectors are opposite , θ = 180˚
A= 4 cm, and B = 3 cm
4 cm , 3 cm
4 – 3 = 1, 1 cm
The magnitude of resultant vector is by simple subscription.
The direction of resultant is same as that greater.
4. If two vectors of same magnitude than direction of resultant with respect to either vector will
be at half angle.
B = 4 45˚ R
45˚
A = 4
At what angle the magnitude of R is same of the two vectors of equal magnitude.
Ans: θ = 120˚
B = 4
θ = 120˚
A = 4
By cosine law:-
| R | = √ A2
+ B2
+ 2AB Cos θ
= √ 42
+ 42
+ 2 X 4 X 4 Cos 120˚

8. 8
= √ 16 + 16 + 32 X – 0.5
= √ 32 – 16
= √ 16
= 4. Ans
Vector addition obey “commutative law” and “associative law”.
 Commutative Law:
A + B = B + A
 Associative Law:
A + ( B + C ) = ( A + B ) + C
Vectors Subtraction:
Also addition of vector.
Same magnitude but opposite direction. Cosine law is same.
| A - B | = √ A2
+ B2
- 2 AB cos θ
1. If two vectors are parallel θ = 0˚
A = 4 cm , B = 3 cm
4 – 3 = 1, 1 cm
Magnitude: Simple subtraction.
Direction: Same as that of given vector.
2. If two vector are perpendicular θ = 90˚
B = 3
90˚
A = 4
The magnitude by pathagorous.
| R | = √ A2
+ B2
3. If two vectors are opposite θ = 180˚
A = 4 cm , B = 3 cm
Magnitude: Simple addition.
Direction: Same as that of greater.

9. 9
Types of Vectors:
Free Vector:
The vectors which can be shifted from one place to another without changing its
magnitude as well as direction.
e.g: 6 cm , or 6 cm
The vector which is displaced parallel to itself.
Negative Vector:
The vector which is has same magnitude but opposite direction.
e.g: 6 cm , 6 cm
Opposite direction
Resultant Vector:
When two or more than two vectors are added than the new vector is called
resultant vector.
Null vector:
The vector whose magnitude is zero and no direction.
When two vectors of same magnitude and opposite direction are added then
resultant vector is called null vector.
Position vector:
The vector which specify the position of a partical.
Coplanar Vector:
The vector which is parallel to a plane is called coplanar vector.
Unit Vector:
The vector whose magnitude is one.
It show only direction.
It is obtain by dividing vector with its magnitude.
 = A / | A |
 = direction of A ( unit vector )

10. 10
A = vector A =˃ magnitude + direction
| A | = magnitude of A.
The angle between same unit vectors is
Î . î => θ = 0
ĵ. Ĵ => θ = 0
The angle between two different unit vectors is
Î . ĵ => θ = 90˚ j
Ĵ . k => θ = 90˚ k i x
K . î => θ = 90˚
Equal Vector:
Two vectors of same magnitude and same direction.
Trigonometry: Tri + gono + metery.
3 + θ = 90˚ + measurement. P H
The study about right angle triangle.
H = The side opposite to angle 90˚ B
P = The side opposite to angle θ
B = The remaining side
Sin θ = P / H perpendicular , hypotenuse , base
Cos θ = B / H
Tan θ = P / B
Tan θ = sin θ / cos θ
Pthagorous theorem :- H2
= B2
+ P2
Resolution of Vector:-
(Resolution means to break up.)

11. 11
The breaking of vectors into its rectangular components.
Ay A Ay
θ 90˚ X
Ax
Cos θ = B /H
Cos θ Ax / A
Ax A Cos θ
Sin θ = P / H
Sin θ = Ay / A
Ay = A Sin θ
Rectangular component Ax and Ay are always perpendicular to each other.
Composition of Vectors:-
H2
= B2
+ P2
A2
= Ax2
+ Ay2
Magnitude: A = √ Ax2
+ Ay2
Tan θ = P / B
Tan θ = Ay / Ax
Additions of Vectors by Rectangular
Component Method:-
If we have given two or more than two vectors and we want to find the magnitude and
direction of resultant then
1. Resolve given vector into X and Y component.
2. Add all X component of given we will get X-component of resultant.

12. 12
Rx = Ax + Bx + Cx
3. Add all Y-component of given we will get the Y-component of resultant .
Ry = Ay + By + Cy
The magnitude of resultant by pathagorous
| R | = √ Rx2
+ Ry2
The direction of resultant by θ
θ = tan-1
Ry / Rx => Ay / Ax.
Vector Multiplication:-
Scalar Product OR Dot Product:-
When two vectors are multiplied in such a way that there product come out as a scalar, such
product is called Scalar product.
B = 4
θ = 60˚
A = 3
A . B = AB Cos θ
e.g:
Work = W = F . S
Power = P = F . V
Electric flux = Ø = E . ΔA
Properties:-
1. If two vectors are parallel θ = 0˚
A . B = AB
2. If two vectors are perpendicular θ = 90˚
A . B = 0
3. If two vectors are opposite θ = 180˚
A . B = - AB
Vector multiplied with itself
A . A = A2
The scalar product of same unit vectors.

13. 13
i . i = 1 X 1 X Cos θ
i . i = 1
i . i = j . j = k . k = 1
Scalar product of different unit vectors always zero.
i . j = 1 X 1 X Cos 90˚
i . j = 0
i . j = j . k = k . i = 0
Commutative law is valid.
A . B = B . A
Distributive law is also valid for scalar product.
A . ( B + C ) = A . B + A . C
Vector Product OR Cross Product:-
When two vectors are multiplied in such a way that there product comes out as vector such
product is called vector product.
A X B = C
| C | =AB Sin θ
The direction of vector product is determined by right hand rule.
The of vector product is always perpendicular to given vector.
e.g: Torque, Angular momentum
Properties:-
1. When two vectors are parallel θ = 0˚.
A X B = 0 ( Null vector)
2. If two vectors are perpendicular θ = 90˚.
A X B = AB
3. If two vectors are opposite θ = 180˚.
A X B = 0 ( Null vector)
The cross product of same unit vector
i X i = j X j = k X k = 0 ( Sin 0˚ = 0 )
Cross product of different unit vector
k X i = j X k = i X j = 1 ( Sin 90˚ = 1 )
i X j = k j X i = -k

14. 14
j X k = i k X j = -i
k X i = j i X k = -j
Commutative law is not valid for vector product
A X B = - B X A ( Opposite direction )
Distribution law is valid for vector product
A X ( B + C ) = A X B + A X C
A X R = D + E
M = M
The magnitude of vector product is equal to the area of parallelogram of given vectors.
B
A
Area is equal to | C | = AB Sin θ .

15. 15
Chapter No : 03
MOTION
Motion:
When body change its position with respect to its surrounding is called Motion.
Types of Motion:
1. Linear Motion: Motion in one direction. Or Motion in straight line.
2. Rotatery Motion: When body moves in circular path around fixed point.
3. Vibrating Motion: To & fro, Or back & forth about mean position.
Rest:
When body does not change its position with respect to its surrounding is called Rest.
Distance (s):
The physical separation of body is called Distance.
S.I unit Quantity Dimension
Meter (m) Scalar L
Displacement ( s ):
The physical separation of body in particular direction .
OR/ Distance cover in particular direction.
OR/ Shortest distance between two points.
S.I unit Quantity Dimension
Meter ( m ) Scalar L
Direction: Same as that of motion.
Distance is the magnitude of displacement.
Speed (v):
The distance covered per unit time. OR/ The ratio of distance and time.
OR/ The rate of change of distance.
 S.I unit: meter per second ( m/s )
 Common unit: kilo meter per hour ( km/h )

Dimension: LT - 1
 Formula: v = s / t
 Km/h change into m/s:
m/s = value x 1000
3600
 m/s change into km/h: km/h = value x 3600
1000

16. 16
Types of Speed:
Uniform Speed: “ Equal distance covered in equal time interval.”
e.g: 5 m 5 m 5 m
1 sec 1 sec 1 sec
Variable Speed: “Different distance covered in equal time interval.”
e.g: 8 m 7 m 5 m
1 sec 1 sec 1 sec
Average Speed: “ Total distance covered per total time.”
e.g: 5 m 5 m 5 m
1 sec 1 sec 1 sec
= 15/3 = 5 m.
Instantaneous Speed: “ The speed measured in very short time interval.”
e.g: 5m 5 m 5 m
1 sec 1 sec 1 sec
“ If average and instantaneous speed are equal, than body moving with uniform speed”.
Velocity ( v ):
The distance covered per unit time in particular direction.
OR/ The ratio of displacement and time.
OR/ The rate of change of displacement.
OR/ the displacement covered per unit time.
S.I unit Quantity Formula Dimension
m/s Vector V = S / t LT - 1
Direction: Same as that of displacement.
Types of Velocity:
Uniform Velocity:
Equal distance covered in equal time interval.
e.g: 5 m 5 m 5 m
1 sec 1 sec 1 sec
Variable Velocity:
Different displacement covered in equal time interval.
e.g: 8 m 7 m 5 m
1 sec 1 sec 1 sec

17. 17
Average velocity:
Total displacement per total time.
e.g: 5 m 5 m 5 m
1 sec 1 sec 1 sec
= 15/3 = 5 m.
Instantaneous Velocity:
Velocity measured in very short time interval.
e.g: 5m 5 m 5 m
1 sec 1 sec 1 sec
“ If average and instantaneous velocity is equal then body is moving with uniform velocity”.
Speed is the magnitude of velocity.
Acceleration ( a ):
The rate of change velocity.
OR/ Change in velocity per unit time.
OR/ The ratio of velocity and time.
S.I unit: m/s2
Other unit: foot/s2
, km/hs ,or km h-1
s-1
Quantity: Vector
Formula: a = Δ V / t.
Direction: a) If v is increasing, then a is same that of v.
b) If v is decreasing, then a is opposite to v .
When velocity is decrease then acceleration is produced is called negative ( -ve ) acceleration or
retardation or deceleration.
Types of Acceleration:
Uniform Acceleration:
Equal change in velocity in equal time interval.
e.g: 5 m /s 5 m/s 5 m/s
1 sec 1 sec 1 sec
e.g: +ve a 15m/s 10 m/s 5 m/s
1 sec 1 sec 1 sec
e.g: 5m 5 m 5 m

18. 18
1 sec 1 sec 1 sec
Variable Acceleration:
Different change in velocity in equal time interval.
20 m/s 12 m/s 5 m/s
e.g: 1 sec 1 sec 1 sec
Average Acceleration:
Total change in velocity per total time interval.
e.g: 5 m /s 5 m/s 5 m/s
1 sec 1 sec 1 sec
= 15/3 = 5 m/s2
.
Instantaneous Acceleration:
Acceleration measured in very short time interval.
“If body moving with uniform acceleration, then average and instantaneous acceleration is
equal”.
Graph:
Distance - time show graph speed.
Displacement – time show graph velocity.
Velocity – time show graph acceleration.
1. Straight line distance time graph show uniform speed.
Curved line distance time graph show variable speed.
2. Straight line S – time graph show same velocity.
Curved line S – time graph show variable velocity.
3. Straight line velocity – time graph show uniform acceleration.
Curved line velocity – time graph show variable acceleration.
Linear Equation of Motion:
Uniform velocity S = Vt
Variable velocity
(1) Vf = vi + at
(2) S = vit + ½ at2
(3) 2as = vf2
+ vi2
Free Fall Motion or Motion Under Gravity:

19. 19
(1) The motion due to the earth attraction.
(2) Free fall motion is good example of uniform acceleration and it is called “ acceleration due
to gravity” represented by “g”.
Gravitational acceleration = g = 9.8m/s2
Different values of “g” :-
In S.I unit: 9.8 m/s2
In C.G.S unit: 980 cm/s2
In F.P.S unit: 32 ft/s2
Mass:
The quantity of matter passes of a body.
OR/ The measure of inertia of body.
OR/ The ratio of force and acceleration.
S.I Unit Quantity Formula Dimetion
Kg Scalar m = f/a M
Force:-
“The agent which change or tends to change in state of body”.
OR/ “The agent which produce acceleration”.
OR/ “The rate of change of momentum”.
OR/ “The product of mass and acceleration”.
 Formula: F = ma ● F = ma => F = mΔv / t => F = ΔP /t.
 Quantity: Vector.
 Unit: kgm /s2
= Newton
 Dimension: M L T -2
 Newton (N): When body of 1 kg mass then accelerated through 1 m / s2
, then applied force is
called 1 N.
 Direction: Same as that of acceleration.
Types of Force:
i. Weight: “The force exerted by earth on the body”.
 Direction: Vertically downward or toward center of earth.
 Formula: W = mg
 Units: Newton.
ii. Reaction: “The force exerted by surface on a body”.

20. 20
 Formula: it is not particular when body is placed on horizontal surface then equal to weight.
R = W = mg
 Direction: Perpendicular to surface.
 Unit: Newton.
iii. Tension: “The force exerted by string on the body”.
 Direction: Along the string
 Formula: It is no same in each situation, when body suspended in string then,
T = W mg.
iv. Friction: “The force which resist / oppose the motion of body.
 Formula: Fs =μ R
 Unit: Newton
 Direction: Opposite to motion.
 It is produced due to rough surface of body.
Momentum:-
The product of mass and velocity. OR Quantity of motion of body.
 S.I unit: kg m / s => N.S
 Formula: P = mv
 Quantity: vector
 Dimension: M L T -1
 Direction: Same as that of velocity.
Law of Conservation of Momentum:-
Total momentum of an isolated system remain always same.
OR/ Total momentum before collision is equal to total momentum after collision.
Isolated system:
A system in which vector sum of all forces acting on bodies always equal to zero.
Cases of tension:-
Motion of bodies connected in string.
Case No: 1:- When both bodies move vertically
Acceleration : ( m1 – m2 / m1 + m2 ) g
Tension: (2 m1 m2 / m1 + m2 ) g
Case No: 2:- One body move vertically other horizontal
Acceleration: ( m1 / m1 + m2 ) g

21. 21
Tension: ( m1 m2 / m1 + m2 ) g
Collision:-
a). Elastic:- The collision in which momentum and K.E both are conserved (same ).
b). Inelastic: - The collision in which momentum is conserved but K.E is not conserved.
Law of Motion:-
First law:-
If body state of rest or moving with uniform velocity. It does not change its state unless acted
by unbalance force.
It is also called “law of inertia”.
It is theoretical and quality in nature.
Inertia:- The property of matter which oppose in the change of state of body.
Second law:-
It is also called “law of cceleration”.
It is mathematical and quantity in nature.
The acceleration is directly proportional to applied force and inversely proportional to mass of body.
a α F / m
a = k F / m
a = F / m k = 1
F = m a
Third law:-
Action and reaction are always equal in magnitude but opposite to direction.
e.g: Walking of man against friction.
Limiting / Static Friction:-
The minimum force at which body start motion.
OR/ The force of friction between two stationary surface in contact is called static friction.
Fs α R
Fs = μ R
Fs = μ m g
It is a self adjusting force.
Co-efficient of Friction ( μ ):-
The ratio of limiting friction to normal reaction.
. μ = Fs / R
It has no dimension, no unit and it depend upon contact of surface.

22. 22
Types:-
1. Sliding 2. Rolling
Always sliding friction greater than rolling.
Viscosity:-
Fraction between two layers of liquid.
Fluid / Viscous drag:-
Fraction between solid and liquid.
Stook’s Law:-
When sphere dropped in liquid, first its velocity is increasing for some time and then its
velocity is uiform.
F = 6 π ɳ Ɣ V
R = Radius of sphere
V = Velocity of sphere
ɳ = Eta ( co-efficient of velocity. )
Inclined Plane:-
“The surface which make certain angle with the horizontal”.
When body placed inclined plane three forces acting on it.
1. Weight: Acting vertically downward.
2. Reaction: Acting perpendicular to surface.
3. Friction: Opposite to motion.
To find the resultant force, weight is resolve into its components.
a. Wx = W Cos θ, it is equal and opposite to R and perpendicular to surface
R = - Wx => R = - W Cos θ
If body is motionless in inclined plane then,
Wy = - F => F = - W Sin θ
If body is moving with acceleration then
Wy > F
Then resultant force is
F = Wy - F
F = W sin θ - F (1)
From 2nd
law of motion
F = m a (2)

23. 23
Comparing equation (1) and (2)
m a = W Sin θ - F
a = m g Sin θ - F
M m
a = g sin θ – f / m
If friction is zero , then
a = g sin θ
 If friction is not present in inclined plane then a is not depend on mass.
 If friction is present then a is depend on mass.
R F
wx = w cos θ
w
wy = w sin θ

24. 24
Chapter NO # 04
Motion In Two Dimension
Project motion:
“When body is thrown certain angle with horizontal and vertical motion is under influence of
gravity”.
OR/ “Motion in two dimension under influence of gravity”.
OR/ “The body which cover behave as curve”.
OR/ “The body which cover horizontal / vertical distance under influence of gravity”.
OR/ “A body motion in which posses both compound of gravity of velocity (horizontal / vertical)”.
Trajectory:
The path fellow by projectile and it is parabolic curve.
 During motion no force act as horizontal direction, therefore horizontal velocity (Vox) remain
same throughout motion, horizontal acceleration (ax = 0) is also zero.
 As weight act in vertical downward direction so vertical velocity is variable.
 Vertical velocity decreasing in upward direction and become zero at max: height and in
downward motion, vertical velocity increasing.
ay = Uniform ( g )
mean vertical acceleration is uniform
ay = g
Projectile we can also defined in other words: “The motion in which Vx = uniform and ay = g
(uniform) then motion is projectile.
OR/ The motion in which horizontal velocity and vertical acceleration are uniform.
OR/ The motion in which horizontal velocity is uniform and vertical velocity is variable.
 Projectile motion does not effected by:
i. Rotation o earth.
ii. Air resistance.
iii. Acceleration due to gravity.
 One side time : t1 = Vo sin θ / t
 Max: height / time of flight : t2 = 2Vo sin θ
g
 Max: height = Vo
2
sin2
θ
2g
 Range (horizontal distance) = R = Vo
2
/ g Rmax = Vo
2
/ g
Range is same at complementary angle.

25. 25
h =
1
2
gt2
t = 2h / g
Uniform Circular Motion:
“When body rotates in circular path in fixed radius with uniform speed”.
a) Angular Displacement:
“The angle made by the rotating particle with respect to its initial axis
S α θ
S = ɤ θ
S = Linear displacement / are length
θ = Angular displacement
θ = S / r
The ratio of are length to radius.
 If has not unit and dimension.
 S.I unit is radius.
One Radius:- When are length and radius of rotating particle are equal, then angular displacement
said to one radian.
1 radian = 57.3˚ => 360 / 2π => 1˚= 0.01745 rad
Circumference of circle: S = 2 π r
2π = 360˚ π/3 = 60˚
π = 180˚ π/4 = 45˚
π/2 = 90˚ π/6 = 30˚
b) Angular Velocity:
“Rate of change of angular displacement”.
W = Δπ / t
W = rad / sec
 Its common unit “rpm” ( resolution per mint )
1 rev = 2π or 360˚
 Convert “rpm” into rad / sec
red / sec = value X 2 π
60
Direction: By right hand rule
S = r θ
S = r θ

26. 26
t t
V = r w
Direction of linear velocity is by tangent line so it is also called tangention velocity.
Linear velocity ( v ) radius, angular v perpendicular to each other.
c) Angular Acceleration (α):
“Rate of change of angular velocity”
α = Δw / t => rad / S2
Direction: If w increasing, then α is parallel to w.
If w is decreasing, then direction of α is opposite to w.
“Relationship between linear and angular acceleration is
V = rw
V = r w
t t
at = r α
Centripetal Acceleration (ac):
“The acceleration produced due to the continuous change in direction of linear velocity”.
ac = V2
/ R
ac = r w2
Direction: Always toward centre of circle.
Centripetal Force ( Fc ):
“The force which responsible for uniform circular motion”.
OR/ “The force which rotate the body in fixed radius with uniform speed”.
OR/ “The force which produced centripetal acceleration”.
Fc = mac (1)
Fc = m v2
(2)
r
Fc = m r w2
(3)
Centrifugal Force:
“It magnitude is always equal to centripetal force and opposite to direction”.
Time Period:
“The time required to complete one revolution or one cycle”.
For one complete revolution,

27. 27
S = 2 π r (1)
V = r w (2)
t = T (3)
S = Vt
2 π r = r w X t
T = 2 π r
r w
T = 2 π
w

28. 28
Chapter NO # 05
Torque Angular Momentum And Equilibrium
Translatory Motion:
“The motion in which axis of frame of reference displaces parallel to itself”.
OR/ “The motion in which constituent particles of the body covers same displacement”.
OR/ “The motion may or may not be in state line”.
Rotatory Motion:
The motion in which constituent particles of the body cover different displacement.
Axis Of Motion:
The line around which body rotates in circular path.
Spin Motion:
The rotatory motion in which axis of rotation inside the body.
e.g: Motion of top and motion of earth around its own axis.
Orbital Motion:
The rotatory motion in which axis of rotation is outside the body.
e.g: The motion of earth around the sun.
Center Of Mass:
The point in the body at which applied force produce linear acceleration but no otation.
OR/ The point in the body at which whole mass concentrated.
OR/ It describe translational motion.
Center Of Gravity:
The point in the body at which whole weight is concentrated.
In a uniform gravitational field center of mass and center of gravity concede each other.
Couple:
When two equal and opposite force acting on a body, but not in the same line produces
couple.
5N 5N
Torque (Moment Of A Force):
The turning effect of force. OR/ The quantity which produce angular acceleration.
It is a vector quantity. It is denoted by symbol ‘τ’.

29. 29
Mathematically:
The vector product of force and moment arm ( d )
Formula
Torque = Force X Moment Arm
τ = F X d
τ = Fd sin θ
Moment Arm:
The shortest distance between point of action of force and center of gravity.
Direction by right hand rule.
It is always perpendicular to force and a .
Its dimension is = M L2
L-2
The rate of change of angular momentum is called torque.
τ = ΔL / t
The rotational analogue of force.
Clock Wise (-ve) Anti clock wise (+ve) / counter c-w
Equilibrium:
When body is in rest or moving with uniform velocity, then it is said to be in equilibrium.
Static Equilibrium:
When body is in state of rest.
e.g: Table
Dynamic Equilibrium:
When body is moving with uniform velocity. e.g: Parachute
First Condition Of Equilibrium:
The sum of all forces acting along X-axis and Y-axis always equal to zero.
Σ Fx = 0, and Σ Fy = 0
Σ F = 0 Translatory equilibrium
Linear momentum is conserved when first condition is satisfied.
Σ P = 0
Second Condition Of Equilibrium:

30. 30
The sum of all torque acting on a body always equal to zero.
Σ τx = 0, and Στy = 0
Σ τ = 0 Rotatory equilibrium
Angular momentum is conserved when second condition is satisfied.
Σ L = 0
Translatory Motion Rotatory Motion
Force is applied.
1st
condition is satisfied.
If Σ F = 0, then linear momentum is conserved.
Torque is applied.
2nd
condition is satisfied.
If Σ τ = 0, then angular momentum is conserved.
Angular Momentum / Vector Product:
The vector product of radius vector and linear momentum
L = r X P
L = rP sin θ
r and P are always perpendicular to each other.
L = rp
L = mvr ( v = r w )
L = m r2
w
Unit of angular momentum is J. sec
W and L are in same direction.
Dimension is M L2
T-1
.

31. 31
Chapter NO # 06
Gravitation
“Force between two masses”.
Universal law of Gravitation:-
The force is directly proportional to product of masses and inversely proportional to the
square distance between them.
F = G m1 m2
r2
G => Universal gravitational constant.
S.I unit => N m2
/ kg2
S.I value => 6.67 X 10-7
Nm2
/ kg2
Dimension is => M-1
L3
T-2
It is found by Cavendish.
G:- When two masses of 1kg each 1m apart, then force between them is called G.
-ve F = Attractive force
+ve F = Repulsive force
Value of G in C.G.S => G = 6.67 X 10-8
dyne cm
Time Increase Decrease
One time
Two time
Three time
Four time
No change
Double / Twice
Triple / Thrice
quadrupled
No change
Half
One third
One fourth
Variation of g with Depth:
Gd = (1- d / Re ) g
The value of g at centre of earth is zero.
Value of g at surface of moon is 1/6th
of g at earth surface.
The value of “g” is maximum at sea level and at surface of earth is 9.8m / s2
.
Weight:-
The force exerted by earth on body.
Apparent Weight:-
Weight is variable quantity.
Its value depend upon location and motion of frame of reference.
If lift is in equilibrium ( a = 0 ), the apparent weight is equal to actual weight.
If lift moving upward with a, then weight increase,
W = mg + ma

32. 32
If lift moving downward with a, then weight decrease,
W = mg – ma
Weightlessness:-
The suition in which apparent weight become zero due to a = g .
When satellite is orbiting around the earth, then satellite of weightlessness is observed, because ac is
balanced by gravitational a to other this by difficulty, artificial gravity is produced by spinning the
satellite.
Radius Of Earth:
Re = 6.4 X 10-6
m
Re = 6400 km => 4000 miles
Mass Of Earth:
Me = 6 X 1024
kg
Me = 6 X 1027
g
Value of Earth:
Ve =
4
3
π Re3
Ve = 1.08 X 1021
m3
Density of Earth:
= M /V
= 5.5 X 103
kg / m3
Variation of g:-
The value of g depend upon distance of object from center of earth.
g = G Me
Re2
Variation of g with attitude ( height ):-
gh = ( 1 – 2h ) g
Re
The value of g is greater at the pole, and it is smaller at the quarter.
 Mass of the sun 1.99 X 1030
kg, thus the mass of sun is 3 X 105
times the mass of the earth.

33. 33
Chapter NO # 07
Work, Power And Energy
Work:-
When force is applied on the body and it covers same displacement then work is said to be
done on the body.
The scalar product of force and displacement.
W = F . d
W = F d Cos θ
Wmax: => at θ = 0˚ F and d parallel
Wmin: => at θ = 90˚ F and d perpendicular
Work done is zero at the θ of 90˚.
Negative work is done when θ = 180˚.
“Work done against gravitational field”, and “walking against friction” are the examples of negative
work done.
S.I unit of work is = J = Nm
CGS unit =Erg = dyne cm
1 J:- When force of 1N is applied on a body and it covers displacement of 1m in the direction of
force.
1 Erg:- When force of 1dyne is applied on a body and it covers displacement of 1cm in the direction
of force.
1 J = 107
Erg
Work done by centripetal force is zero.
Work done in any close path is always zero.
Work done is independent of the path followed by the body.
Power:-
The rate of doing work or work done per unit time.
P =w / t
The scalar product of force and velocity.
P = F . V
P = FV Cos θ
S.I unit => watt = J / s
Watt = Nm / s
1 watt :- When 1J work is done in 1 sec; then power is said to be 1 watt.

34. 34
When 1N is applied on the body and it moves with speed of 1m/s in the direction of force then power
is said to be one watt.
Common unit : hp = horse power
1 hp =746 watt.
Energy:-
The ability of doing work.
K.E :- The energy due to motion is called Kinetic Energy.
K.E =
1
2
m v2
P.E :- The energy due to position.
Gravitational P.E = mgh
Downward Upward
K.E increase
P.E decrease
P.E = K.E
K.E decrease
P.E increase
K.E = P.E
Law Of Conservation Of Energy:-
The energy neither be created nor be destroyed but it can only changes from one form to
another.

35. 35
Chapter NO # 08
Wave, Motion And Sound
1) Wave:-
The periodic disturbance of the particles in a medium.
Wave carry energy.
Energy ∞ √Amplitude
Transverse wave Longitudinal wave
i. Waves in which particles of the medium
vibrate perpendicular to the direction of
propagation of wave.
ii. No need of medium for propagation.
iii. e.g: Light waves, electromagnetic waves,
waves in string, water waves.
i. Waves in which particles of the
medium vibrate parallel to the
direction of propagation.
ii. Medium is compulsory.
iii. e.g: Sound waves, mechanical waves,
etc.
2) Periodic Motion:-
The motion which is repeated after equal time also known as vibratory motion.
Vibration:
One complete round trip of a vibrating particle about its mean position.
Frequency:
No; of vibrations executed in 1 second.
Unit: Vib / Sec = Hertz (Hz).
OR Reciprocal of time period, f = 1 / T.
Time Period:
Time required to complete one vibration.
Time period and frequency are reciprocal to each other, i.e , T = 1 / f .
S.I Unit is second.
Wave Length:
Minimum distance between two adjacent “crest” or “trough”.
OR The minimum distance between two adjacent identical points.
Sign: λ = lambda.
S.I unit: m, A˚
A˚ = 10-10
m
c c c c c c
t t t t t

36. 36
Mean Position: Midpoint or equilibrium position.
Extreme Position: Returning point.
In every vibrating motion one mean and two extreme position.
Displacement ( X ):-
Distance of the vibrating particles from its mean position.
Direction always away from mean position.
Amplitude ( Xo ):-
Maximum displacement of the vibrating particles.
The distance from mean to extreme position.
Node:-
The point at which amplitude is zero.
Antinode:-
The point at which amplitude is maximum.
Relation between ⱴ and λ :-
ⱴ ∝ 1 / λ
ⱴ = V / λ
λ = V / ⱴ
Simple Harmonic Motion ( S.H.M ):-
The motion in which acceleration is directly proportional to the displacement and always
directed towards mean position.
Mathematically: a ∝ - x
Direction of acceleration is towards mean position.
Acceleration at mean position is zero.
Acceleration at extreme position is maximum.
Fig: x = 0 x
Elastic Restoring Force:-
The force exerted by the spring on the body.
Hook’s Law:-
The E.R.Force is directly proportional to the displacement and always directed towards mean
position.

37. 37
Fs ∝ - x
1. Fs = - Kx
K = Spring or force constant. Unit is Nm-1
.
Body connected in spring executing SHM:
2. Time period T = 2π √ m/ k
3. K.E =
1
2
K ( x0
2
– x2
)
4. P.E =
1
2
K x2
5. a = - Kx / m
6. w = √ k / m
At mean position At extreme position
K.E(max) = ½ K Xo
2
P.E(min) = 0
T.E remain same = ½ K Xo
2
x = 0
a = 0
P.E = 0
V = Maximum
K.E = maximum
Fs = 0, minimum
K.E(min) = 0
P.E(max) = ½ K Xo
2
Elasticity depend upon spring
x = Maximum
a = Maximum
P.E = Maximum
V = 0
K.E = 0
Fs = maximum
Simple Pendulum:-
It is used to check the value of “g”.
T = 2π √ l / g
Restoring force is responsible for motion.
Re f = m g Sin θ
“T” depends upon length not on mass.
Condition of S.H.M:-
(1) There must be inertia.
(2) There must be restoring force.
(3) Acceleration is directly proportional to – x.
Frequency of pendulum = F = 1 √ g / r
2π
“T” at equator is maximum for pendulum.

38. 38
Pendulum is very slow at center of earth.
Second pendulum: T 2 sec and ⱴ = 0.5Hz.
Pendulum is fast at surface of earth.
Stationary Waves:-
When one or both ends of a string are fixed, then waves in it are stationary or standing
waves.
They move in finite distance.
They do not transmit energy.
Travelling Waves:-
Waves which move in infinite distance. They transmit energy.
Acoustics:-
The study about the properties and production of sound waves.
Audible: 20 Hz ------------ 20 KHz , Voice which is listen.
Infrasonic: Below 20 Hz, not listenable.
Ultrasonic: Above 20 KHz, not listenable.
Speed of sound: V = 330 to 340 m /s.
V ∝ √ T
V = √Elasticity / Density
“V” changes 0.6 m/s or 60 m/s per degree change in temperature.
Properties of Sound:-
1. Loudness:-
The auditory sensation or intensity level of sound.
Unit: Decibel => db formula: loudness = E / At
Definition: The energy transmitted per unit area per unit time.
2. Pitch:-
It is ∝ to the ⱴ of sound.
By which we can differentiate between grave and shrill sound.
Unit is Hz.
υ of shrill is more than grave.
3. Quality:-
The properly sound by which we distinguish two sounds of same loudness and same pitch but
from two different instruments.
4. Beats:-

39. 39
The slight change in the frequency of sound wave in the same phase.
Range => 6 Hz or less than 6 Hz.
5. Musical Sound:-
Regular, symmetrical and pleasant sensation of sound.
6. Noise:-
Irregular, unpleasant and non-symmetrical and random fluctuation of sound.
Doppler Effect:-
The apparent change in the frequency of sound due to the relative motion of source of sound
and observer.
Application:-
i. It is used to check the speed of automation.
ii. Used in radius.

40. 40
Chapter NO # 09
Nature Of Light
Light:-
Electromagnetic wave. Light has dual nature. Some times like it behave like wave and some
times like a particle.
e.g: For wave nature: Interference, diffraction, polarization, reflection, and refraction of light.
e.g: For particle nature: Photoelectric effect, pair production, Compton effect etc.
Speed of light:- C = 3 X 108
m / s
OR C = 3 X 105
km / s
OR C = 186000 miles / s
Light year is the unit of distance.
Distance covered by light in one year is called one light year.
1 year = C X 365 X 24 X 60 X 60.
Wave Front:-
The surfaces in which light propagates are called wave front.
There are perpendicular to the propagation of light.
Plane Wave Front:-
The wave front in which light travels in straight line.
The source of light and screen are at infinite distance. e.g.: Laser.
It is two dimensional.
Spherical Wave Font:-
The wave front in which light propagates in circle. i.e.: in all direction.
OR Wave front in which light propagates in all possible directions.
Source of light and screen are at finite distance.
It is in three dimensional.
Light revolve six time around earth in one second.
Interference of Light:-
The super position or overlapping of two light waves is called interference of light.
Constructive Destructive
1) When crest of 1st
wave falls on the crest
of 2nd
wave and trough of the 1st
wave
falls on the trough of 2nd
wave.
2) Bright fringes are obtained.
3) The amplitude and intensity of resultant
1) Vice versa
2) Dark fringes are produced.
3) Vice versa

41. 41
wave increases intensity ∝ amplitude.
4) Path difference is equal to integral
multiple of wave length.
d Sin θ = m 𝜆
4) Path difference is equal to integral
multiple of 𝜆 + ½ of wave length.
d Sin θ = m + ½ ) X 𝜆
d Sin θ = m 𝜆 +
𝜆
2
Young’s Double Slit Experiment ( By: Thomas Young ):-
It is used to calculate “𝜆” of light.
𝛥𝑥 = Fringe spacing
d = distance between slits
m = No of fringes
l = distance between slits and screen.
Fringe Spacing:-
Distance between two alternate dark or bright fringes.
𝛥𝑥 = 𝜆 𝑙 / d
Distance between slits must be in order of “𝜆" of light.
Condition’s of Interference:-
Source must be co-horrent and mono-chromatic.
Michelson’s Interference:-
Device by which we measure “𝜆" of light.
Diffraction:-
The bending of light around the edges of an obstruct.
In interference fringes spacing are equally spaced and in diffraction spacing are not equally spaced.
Types of Diffraction:-
1. Fresnel:-
When source of light and screen are at finite distance.
Spherical wave fronts are observed.
2. Fraunhofer:-
When source of light and screen are at infinite distance.
Plane wave fronts are observed.
Polarization of Light:-
The method by which we distinguish longitudinal and transverse wave.

42. 42
Refraction of Light:-
The changing of direction of light due to the change in medium.
Transparent:-
Material through which light can pass.
Opaque:-
The material through which light cannot pass.
Translucent:-
Moderate level of transparent and opaque.
Luminous:-
The source which has its own light. e.g. Sun.
Non-Luminous:-
Source which have not its own light. e.g. Moon.
VIBGYOR:-
Mean colour Green.
𝜆 increases from V to R and ⱴ decreases from V to R.

43. 43
Chapter NO # 10
Geometrical Optics
Convex Lens:-
Lens which is thicker at the middle and thinner at the edges.
OR Converging lens.
Concave lens:-
Lens which is thinner at the middle and thicker at the edges.
OR Diverging lens.
c f f c
Optical Centre:-
Mid point of lens.
Radius of Curvature:-
The distance from centre of curvature to optical centre. ( OC distance ). C = 2f.
Principle Focus:-
Mid point of radius of curvature.
Focal Length:-
Distance from optical centre to focus.
Principle Axis:-
The line joining the two centre of curvature.
Focal length is ½ of radius.
Ray’s Passing Through lenses:
1. Converging OR Convex Lens:-
For Convex:
i. At focus parallel ray’s are intersected
2f f f 2f

44. 44
ii. Ray’s passing from optical travels parallel to principle axis
f f
iii. Ray’s passing from optical centre. Direction remains same.
For Concave:-
i. Parallel Ray’s Diverge
F
ii. Ray’s passing from optical centre. Direction remains same.
2f f f 2f
Image formation through convex lens:-
1. When body is placed at infinite distance
2f f f
2. Away from “2F” ( Camera )
o

45. 45
2f f f 2f
Image formed is
i. Dimensioned
ii. Real
iii. Inverted
iv. Between f and 2f.
3. At 2f ( Photostat Machine ):
f f 2f
2f
Image formed is
i. Equal in size.
ii. At 2f.
iii. Real.
iv. Interval.
4. When body is placed between “f” and “2f” ( Projector ):
2f f f 2f
Image formed is
i. Magnified
ii. Real
iii. Inverted
iv. Away from 2f.
5. When body is placed at “f” ( Spot light ):
F
Image formed is

46. 46
i. Very magnified
ii. At infinite distance
iii. Inverted
iv. Real
6. When body is placed within “f”
Image formed is
i. Erect
ii. Virtual ( Imaginary )
iii. Magnified
iv. At the same side of object.
Image formed by concave lens:
Within F
i. Diminished
ii. Erect
iii. Virtual.
Real Image Virtual Image
i. It form’s due to real intersection of
ray’s.
ii. Inverted
iii. Can be brought on screen.
i. It form’s due to virtual intersection of
ray’s.
ii. Erect
iii. Can not be brought on screen.
Lens Formula:-
1
𝑓
=
1
𝑝
+
1
𝑞
p = Object distance
q = Image distance

47. 47
f = Focal length
Sign Convention:-
f +ve = convex , q +ve = Real image.
f –ve = concave , q –ve = Virtual image.
p +ve = real object distance , p –ve = Virtual object distance.
Magnification:-
The ratio of image distance to the object distance. i.e. 𝑀 = 𝑞/𝑝
The ratio of image height to object height. i.e. 𝑀 =
𝐻𝑖
𝐻𝑜
𝐻𝑖
𝐻𝑜
= 𝑞/𝑝 No unit
M = 1 :- Equal in size.
M < 1 :- Diminished.
M > 1 :- Magnified.
M +ve :- Real image.
M –ve :- virtual image.
Virtual magnified: - Convex.
Virtual diminished:- Concave.
Power Of The Lens:-
It is reciprocal to the focal length.
𝑃 =
1
𝑓
Unit: Diopter.
1 Diopter: When the focal length of the lens is 1 m then power is 1 diopter.
Combination Of Lenses:-
f1 f2 f
(This lens is equivalent )
1
𝑓
=
1
𝑓1
+
1
𝑓2
f = Focal length of equivalent lens.

48. 48
Power of equivalent lens is: P = P1 + P2
P =
1
𝑓
When 2 lenses are combined then their “F” decreases and power increases.