CBSE 11 Physics Derivations

TickleYourMindPhysicsWithHimanshu
Newton’s Laws of Motion
Objects at Rest
Simply put, things tend to keep on doing what they’re
already doing.
• Objects in a state of rest tend to remain at rest.
• Only a force will change that state.
Newton’s Law of Inertia
Objects in Motion
Now consider an object in motion.
• In the absence of forces, a moving object tends
to move in a straight line indefinitely.
• Toss an object from a space station located in
the vacuum of outer space, and the object will
move forever due to inertia.
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Mass vs Weight
Mass Is Not Weight
Mass is often confused with weight.
• We often determine the amount of
matter in an object by measuring
its gravitational attraction to Earth.
However, mass is more
fundamental than weight.
• Mass is a measure of the amount
of material in an object. Weight,
on the other hand, is a measure
of the gravitational force acting on
the object.
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Projectile Motion-Horizontal Motion

Friction – Static and Kinetic
frictionstaticoftcoefficien
Ff
s
sNs



The Force of Static Friction
keeps a stationary object at
rest!
Once the Force of Static Friction
is overcome, the Force of Kinetic
Friction is what slows down a
moving object!
frictionkineticoftcoefficien
Ff
k
kNk





Uniform Circular Motion – Centripetal Acceleration

Impulse Momentum Theorem

Derivation of Newton's Third Law from 2nd Law

Motion of Car on level road

Motion of Car on banked road

Work Energy Theorem for Constant Force

Work Energy Theorem for Variable Force

Elastic Collision
'
1u '
2u
1u
2u
v
2v1v
'
1v '
2v







During
collision
Long
before
collision
Long
after
collision
Total linear momentum before collision =
Total linear momentum after collision
   1 1 1 2 2 2m u - v =m v -u
uur uur uur uur
By conservation of kinetic energy,
Total kinetic energy before collision = Total kinetic energy after collision
   2 2 2 2
1 1 1 2 2 2m u - v =m v -u
Relative velocity before collision = Relative velocity after collision
1 2 2
1 1 2
1 2 1 2
m - m 2m
v = u + u
m +m m +m
   
      
1 2 1
2 1 2
1 2 1 2
2m m - m
v = u + u
m +m m +m
   
      
1 1 2 2 1 1 2 2m u + m u = m v + m v
uur uur uur uur
   1 1 1 2 2 2m u - v = m v - u
uur uur uur uur
2 2
1 1 2 2
1 1
m u + m u
2 2
2 2
1 1 2 2
1 1
m v + m v
2 2
   2 2 2 2
1 1 1 2 2 2m u - v = m v - u
'
1u '
2u
1u
2u
v
2v1v
'
1v '
2v







During
collision
Long
before
collision
Long
after
collision

Inelastic Collision and Perfectly Inelastic Collision
'
1u '
2u
1u
2u
v
2v1v
'
1v '
2v







During
collision
Long
before
collision
Long
after
collision
Total linear momentum before collision =
Total linear momentum after collision
   1 1 1 2 2 2m u - v =m v -u
uur uur uur uur
By conservation of kinetic energy,
Total kinetic energy before collision is not equal to Total kinetic energy after collision
For perfectly inelastic collision, bodies stuck after colliding.
 
 
1 1 2 2
1 1 2 2 1 2
1 2
m u m u
m u m u m m v or v
m m

   

 2 2 2
1 1 2 2 1 2
1 1 1
E = m u m u m m v
2 2 2
  Loss in Energy:

Relation between angular velocity and linear velocity

Derivation of Centre of Mass Coordinates

Conservation of Angular Momentum

Theorem of Parallel Axes

Theorem of Perpendicular Axes

COM of a Rod length L

Moment of Inertia of Cylinder

Moment of Inertia of Rod of length l

Moment of Inertia of Uniform Disc

Power in Rotational Motion

Kinetic Energy in Rolling Motion Inclined Plane

Acceleration in inclined plane motion

Kepler’s Third Law

Escape Velocity

Orbital Velocity

Total Energy of Satellite

Variation of g with depth

Variation of g with height

Derivation of Gravitational Potential Energy

Stress Strain Curve
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Young Modulus

Shear Modulus
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Bulk Modulus
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Variation of Pressure with Height
Pressure P at a depth h below the surface of a liquid open to the atmosphere is
greater than atmospheric pressure
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Buoyant Force
• Upward force that keeps things
afloat is equal to the magnitude
of the weight of fluid displaced by
the body
• Archimedes principle
• The magnitude of the buoyancy
force always equals the weight of
the fluid displaced by the object.
MggVB objectfluid  
M is the mass of the displaced fluid and not the mass of the object

Bernoulli’s Theorem

Torricelli's Law
For an open tank, the speed of liquid coming out through
a hole a distance h below the surface is equal to that
acquired by an object falling freely through a vertical
distance h.

Stokes Law

Viscosity and Reynold’s Number

Surface energy

Excess Pressure inside Drop and Bubble

Capillary Rise

Terminal Velocity

Linear Expansion, Area Expansion and Volume Expansion
Linear Expansion: Consider a rod of length l1 at a temperature T1. Let it be a heated to a
temperature T2 and the increased length of the rod be l2 then
l2 l1 (1 t)
  Coefficient of linear expansion and 2 1  t T T
Area Expansion: If A1 is the area of solid at T1 C and A2 is the area at T2C . Then

Coefficient of Volume Expansion of Gas

Relation between α, β, γ

Conduction

Thermal Stress

Density of Water vs Temperature

Heat Transfer Mechanisms

Specific Heat and Latent Heat

Graph of Change of State with Temperature

Gas Laws
 Pressure and volume are inversely related at
constant temperature.
 PV = K
 P1V1 = P2V2
Boyle’s Law
 Volume of a gas varies directly with the
absolute temperature at constant pressure.
 V = KT
 V1 / T1 = V2 / T2
Charles’ Law
At constant temperature and pressure, the volume
of a gas is directly related to the number of moles.
V = K n
V1 / n1 = V2 / n2
Avogadro’s Law
 At constant volume, pressure and
absolute temperature are directly
related.
 P = k T
 P1 / T1 = P2 / T2
Gay-Lussac Law
Dalton’s Law
 The total pressure in a container is the sum of the pressure each gas would exert
if it were alone in the container. The total pressure is the sum of the partial
pressures.
 PTotal = P1 + P2 + P3 + P4 + P5 ... (For each gas P = nRT/V)

Newton’s Law of Cooling

Work Done Isothermal Process

Work Done in Adiabatic Process

Work Done in Isobaric Process

Work Done in Isochoric Process

Relation between Cp and Cv

Synopsis of all Thermodynamic Process

Efficiency of Heat Engine

Efficiency of Heat Pump (Refrigerator)

Carnot Engine

Pressure by an ideal gas on walls of container

Law of Equipartition

Mean Free path

Vrms, Vav, Vmp of Ideal Gas

Time Period of Spring Mass System by Force Equation
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Time Period of Spring Mass System by Energy Equation

Conservation of Energy in SHM

Time Period of Simple Pendulum – Linear SHM

Time Period of Simple Pendulum – Rotational SHM

Damped SHM : Derivation of Energy and Amplitude

Forced Oscillations and Resonance

Derivation of Displacement Relation : Travelling Wave

Speed of a Transverse Wave on Stretched String

Speed of a Longitudinal Wave Speed of Sound
  

B
v (Where B is Bulk Modulus of the medium and v is velocity of wave)


Y
v


B
v
FOR SOLIDS, speed of sound wave is given by
Where Y is young’s modulus of the solid and p is density of solid
where B = bulk modulus of liquid.
FOR LIQUIDS, speed of sound wave is given by

Speed of Sound in Gas

Principle of Superposition and Resultant Intensity

Reflection AND Refraction of Waves

Equation of Standing Wave

Standing Waves: Open at Both End

Standing Waves: Open at one End

String fixed at both Ends

String open at one End

Beats: Derivation of Equation
When two sound waves of same amplitude travelling in a same direction with slightly different
frequencies superimpose, then intensity varies periodically with time. This effect is called
Beats.

Beat Frequency

Doppler Effect: Source Moving Towards Observer

Doppler Effect: Observer Moving Towards Source

Relative motion between Source and Observer in Doppler Effect

CBSE 11 Physics Derivations

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