Topics
Physical World and Measurement
Physical World
Units and Measurements
 International System of Units
 Measurement of Length
 Measurement of Mass
 Measurement of Time
 Accuracy Precision of Instruments and Errors in Measurement
 Significant Figures
 Dimensions of Physical Quantities
 Dimensional Formulae and Dimensional Equations
 Dimensional Analysis and Its Applications
 Need for Measurement
 Units of Measurement
 Fundamental and Derived Units
 Length, Mass and Time Measurements
 Introduction of Units and Measurements
Kinematics
Motion in a Plane
 Scalars and Vectors
 Multiplication of Vectors by a Real Number
 Addition and Subtraction of Vectors — Graphical Method
 Resolution of Vectors
 Vector Addition – Analytical Method
 Motion in a Plane
 Motion in a Plane with Constant Acceleration
 Projectile Motion
 Uniform Circular Motion
 General Vectors and Their Notations
 Motion in a Plane  Average Velocity and Instantaneous Velocity
 Rectangular Components
 Scalar and Vector Product of Vectors
 Relative Velocity in Two Dimensions
 Cases of Uniform Velocity
 Cases of Uniform Acceleration Projectile Motion
 Motion in a Plane  Average Acceleration and Instantaneous Acceleration
 Angular Velocity
 Introduction
Motion in a Straight Line
 Position, Path Length and Displacement
 Average Velocity and Average Speed
 Instantaneous Velocity and Speed
 Kinematic Equations for Uniformly Accelerated Motion
 Acceleration
 Relative Velocity
 Elementary Concepts of Differentiation and Integration for Describing Motion
 Uniform and NonUniform Motion
 Uniformly Accelerated Motion
 Positiontime, Velocitytime and Accelerationtime Graphs
 Motion in a Straight Line  Positiontime Graph
 Relations for Uniformly Accelerated Motion (Graphical Treatment)
 Introduction
Laws of Motion
 Aristotle’s Fallacy
 The Law of Inertia
 Newton'S First Law of Motion
 Newton’s Second Law of Motion
 Newton's Third Law of Motion
 Conservation of Momentum
 Equilibrium of a Particle
 Common Forces in Mechanics
 Circular Motion
 Solving Problems in Mechanics
 Static and Kinetic Friction
 Laws of Friction
 Inertia
 Intuitive Concept of Force
 Dynamics of Uniform Circular Motion  Centripetal Force
 Examples of Circular Motion (Vehicle on a Level Circular Road, Vehicle on a Banked Road)
 Lubrication  (Laws of Motion)
 Law of Conservation of Linear Momentum and Its Applications
 Rolling Friction
 Introduction
Work, Energy and Power
 Introduction of Work, Energy and Power
 Notions of Work and Kinetic Energy: the WorkEnergy Theorem
 Kinetic Energy
 Work Done by a Constant Force and a Variable Force
 Concept of Work
 The Concept of Potential Energy
 The Conservation of Mechanical Energy
 Potential Energy of a Spring
 Various Forms of Energy : the Law of Conservation of Energy
 Power
 Concept of Collisions
 Non  Conservative Forces  Motion in a Vertical Circle
Motion of System of Particles and Rigid Body
System of Particles and Rotational Motion
 Motion  Rigid Body
 Centre of Mass
 Motion of Centre of Mass
 Linear Momentum of a System of Particles
 Vector Product of Two Vectors
 Angular Velocity and Its Relation with Linear Velocity
 Torque and Angular Momentum
 Equilibrium of Rigid Bodies
 Moment of Inertia
 Theorems of Perpendicular and Parallel Axes
 Kinematics of Rotational Motion About a Fixed Axis
 Dynamics of Rotational Motion About a Fixed Axis
 Angular Momentum in Case of Rotation About a Fixed Axis
 Rolling Motion
 Momentum Conservation and Centre of Mass Motion
 Centre of Mass of a Rigid Body
 Centre of Mass of a Uniform Rod
 Rigid Body Rotation
 Equations of Rotational Motion
 Comparison of Linear and Rotational Motions
 Values of Moments of Inertia for Simple Geometrical Objects (No Derivation)
Gravitation
 Kepler’S Laws
 Universal Law of Gravitation
 The Gravitational Constant
 Acceleration Due to Gravity of the Earth
 Acceleration Due to Gravity Below and Above the Surface of Earth
 Acceleration Due to Gravity and Its Variation with Altitude and Depth
 Gravitational Potential Energy
 Escape Speed
 Earth Satellites
 Energy of an Orbiting Satellite
 Geostationary and Polar Satellites
 Weightlessness
 Escape Velocity
 Orbital Velocity of a Satellite
Properties of Bulk Matter
Mechanical Properties of Fluids
 Concept of Pressure
 Pascal's Law
 Variation of Pressure with Depth
 Atmospheric Pressure and Gauge Pressure
 Hydraulic Machines
 STREAMLINE FLOW
 Bernoulli’S Principle
 Viscosity
 Reynolds Number
 Surface Tension
 Effect of Gravity on Fluid Pressure
 Terminal Velocity
 Critical Velocity
 Excess of Pressure Across a Curved Surface
 Introduction to Fluid Machanics
 Archimedes' Principle
 Stokes' Law
 Equation of Continuity
 Torricelli'S Law
Thermal Properties of Matter
 Temperature and Heat
 Measurement of Temperature
 Idealgas Equation and Absolute Temperature
 Thermal Expansion
 Specific Heat Capacity
 Calorimetry
 Change of State  Latent Heat Capacity
 Conduction
 Convection
 Radiation
 Newton’s Law of Cooling
 Qualitative Ideas of Blackbody Radiation
 Wein'S Displacement Law
 Stefan's Law
 Anomalous Expansion of Water
 Liquids and Gases
 Thermal Expansion of Solids
 Green House Effect
Mechanical Properties of Solids
Thermodynamics
 Thermal Equilibrium
 Zeroth Law of Thermodynamics
 Heat, Internal Energy and Work
 First Law of Thermodynamics
 Specific Heat Capacity
 Thermodynamic State Variables and Equation of State
 Thermodynamic Processes
 Heat Engines
 Refrigerators and Heat Pumps
 Second Law of Thermodynamics
 Reversible and Irreversible Processes
 Carnot Engine
 Isothermal Processes
 Adiabatic Processes
Behaviour of Perfect Gases and Kinetic Theory of Gases
Kinetic Theory
 Molecular Nature of Matter
 Behaviour of Gases
 Equation of State of a Perfect Gas
 Work Done in Compressing a Gas
 Introduction of Kinetic Theory of an Ideal Gas
 Kinetic Interpretation of Temperature
 Law of Equipartition of Energy
 Specific Heat Capacities  Gases
 Mean Free Path
 Kinetic Theory of Gases  Concept of Pressure
 Kinetic Theory of Gases Assumptions
 rms Speed of Gas Molecules
 Degrees of Freedom
 Avogadro's Number
Oscillations and Waves
Oscillations
 Periodic and Oscillatory Motions
 Simple Harmonic Motion
 Simple Harmonic Motion and Uniform Circular Motion
 Velocity and Acceleration in Simple Harmonic Motion
 Force Law for Simple Harmonic Motion
 Energy in Simple Harmonic Motion
 Some Systems Executing Simple Harmonic Motion
 Damped Simple Harmonic Motion
 Forced Oscillations and Resonance
 Displacement as a Function of Time
 Periodic Functions
 Oscillations  Frequency
Waves
notes
Atmospheric Pressure

The pressure exerted by the weight of the atmosphere.

The atmosphere is a mixture of different gases. All these gas molecules together constitute some weight. By virtue of this weight, there is some pressure exerted by the atmosphere on all the objects.

This pressure is known as atmospheric pressure.

Value of atmospheric pressure at sea level is 1.01 x10^{5}

1atm = 1.01 x 10^{5}Pa
A long glass tube closed at one end and filled with mercury is inverted into a trough of mercury as shown in Fig. This device is known as the ‘mercury barometer’.
The space above the mercury column in the tube contains only mercury vapor whose pressure 'P' is so small that it may be neglected. Thus, the pressure at Point A=0.
The pressure inside the column at Point 'B' must be the same as the pressure at Point 'C', which is atmospheric pressure, 'Pa'.
Pa = ρgh
where ρ is the density of mercury and h is the height of the mercury column in the tube.
A pressure equivalent of 1 mm is called a torr (after Torricelli).
1 torr = 133 Pa.
The mm of Hg and torr are used in medicine and physiology.
In meteorology, a common unit is 'bar' and 'millibar'.
1 bar = 10^{5} Pa
Gauge Pressure:

Pressure difference between the system and the atmosphere.

From relation P = Pa + ρgh where P= pressure at any point, Pa = atmospheric pressure.

We can say that Pressure at any point is always greater than the atmospheric pressure by the amount ρgh.

P  Pa = ρgh where

P= pressure of the system, Pa= atmospheric pressure,

(P  Pa) = pressure difference between the system and atmosphere.

hρg = Gauge pressure.
An open tube manometer is a useful instrument for measuring pressure differences. It consists of a Utube containing a suitable liquid i.e., a lowdensity liquid (such as oil) for measuring small pressure differences and a highdensity liquid (such as mercury) for large pressure differences.
One end of the tube is open to the atmosphere and the other end is connected to the system whose pressure we want to measure.
The pressure 'P' at 'A' is equal to the pressure at point 'B'. What we normally measure is the gauge pressure, which is (P − Pa), given by equation Pa = ρgh and is proportional to manometer height h.
The pressure is the same at the same level on both sides of the Utube containing a fluid. For liquids, the density varies very little over wide ranges in pressure and temperature and we can treat it safely as a constant for our present purposes. Gases, on the other hand, exhibit large variations of densities with changes in pressure and temperature. Unlike gases, liquids are, therefore, largely treated as incompressible.
Absolute Pressure

Absolute pressure is defined as the pressure above the zero value of pressure.

It is the actual pressure that a substance has.

It is measured against the vacuum.

Absolute pressure is measured relative to absolute zero pressure.

It is the sum of atmospheric pressure and gauge pressure.

P = Pa + hρg where P = pressure at any point, Pa = atmospheric pressure and hρg= gauge pressure.

Therefore P = Pa + Gauge Pressure. Where P = absolute pressure.

It is measured with the help of a barometer.
Problem: The density of the atmosphere at sea level is 1.29 kg/m^{3}. Assume that it does not change with altitude. Then how high would the atmosphere extend?
Answer:
From equation: `"P" = "P"_a +rho"gh"`
`rho"gh"` = 1.29kg/m^{3} x 9.8m/s^{2} x hm = 1.01 x 10^{5} Pa
`therefore` h = 7989m`~~`8 km
In reality, the density of air decreases with height. So does the value of g. The atmospheric cover extends with a decreasing pressure of over100 km. We should also note that the sealevel atmospheric pressure is not always 760 mm of Hg. A drop in the Hg level by 10 mm or more is a sign of an approaching storm.
Problem: At a depth of 1000 m in an ocean (a) what is the absolute pressure? (b) What is the gauge pressure? (c) Find the force acting on the window of 20 cm × 20 cm of a submarine at this depth, the interior of which is maintained at sealevel atmospheric pressure. (The density of seawater is 1.03 × 10^{3 }kgm^{3},g = 10ms^{–2}.)
Answer:
Here h = 1000m and `rho` = 1.03 x 10^{3 }kgm^{3}
(a) From Eq. P2  P1 = `rho`gh, absolute pressure
`"P" = "P"_a + rho"gh"`
=`1.01 xx 10^5"Pa" + 1.03 xx 10^3"kgm"^3xx10"ms"^2xx1000"m"`
`=104.01 xx 10^5"Pa"`
`~~104"atm"`
(b) Gauge pressure is `"P"  "P"_a=rho"gh"="P"_g`
`"P"_g = 1.03 xx 10^3"kg m"^3xx10"ms"^2xx1000"m"`
`=103xx10^5 "Pa"`
`~~103 "atm"`
(c) The pressure outside the submarine is P = P_{a} + ρgh and the pressure inside it is Pa. Hence, the net pressure acting on the window is gauge pressure, Pg = ρgh. Since the area of the window is A = 0.04 m^{2}, the force acting on it is
F = PgA = (10^{3} × 10^{5} Pa) × 0.04 m^{2} = 4.12 × 10^{5} N