Dimensional Analysis and Its Applications

Physical World

• What is Science?
• The Scientific Method
• What is Physics?
• Branches of Physics
• Scope and Excitement of Physics
• Physics Related to Technology and Society
• Nature of Physical Laws
• Fundamental Forces in Nature

Units and Measurements

• International System of Units
• Measurement of Length
• Measurement of Mass
• Measurement of Time
• Accuracy, Precision and Least Count of Measuring Instruments
• Errors in Measurements
• 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

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 (Average and Instantaneous)
• Relative Velocity
• Elementary Concept of Differentiation and Integration for Describing Motion
• Uniform and Non-uniform Motion
• Uniformly Accelerated Motion
• Position-time, Velocity-time and Acceleration-time Graphs
• Position - Time Graph
• Relations for Uniformly Accelerated Motion (Graphical Treatment)
• Introduction of Motion in One Dimension

Motion in a Plane

• Scalars and Vectors
• Multiplication of Vectors by a Real Number or Scalar
• 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 (UCM)
• General Vectors and Their Notations
• Motion in a Plane - Average Velocity and Instantaneous Velocity
• Rectangular Components
• Scalar (Dot) and Vector (Cross) 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 of Motion in One Dimension

Laws of Motion

Work, Energy and Power

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 Body
• 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

Mechanical Properties of Solids

• Elastic Behaviour of Solid
• Stress and Strain
• Hooke’s Law
• Stress-strain Curve
• Young’s Modulus
• Determination of Young’s Modulus of the Material of a Wire
• Shear Modulus or Modulus of Rigidity
• Bulk Modulus
• Application of Elastic Behaviour of Materials
• Elastic Energy

Mechanical Properties of Fluids

• Thrust and Pressure
• Pascal’s Law
• Variation of Pressure with Depth
• Atmospheric Pressure and Gauge Pressure
• Hydraulic Machines
• Streamline and Turbulent Flow
• Applications of Bernoulli’s Equation
• Viscous Force or Viscosity
• Reynold's Number
• Surface Tension
• Effect of Gravity on Fluid Pressure
• Terminal Velocity
• Critical Velocity
• Excess of Pressure Across a Curved Surface
• Introduction of Mechanical Properties of Fluids
• Archimedes' Principle
• Stoke's Law
• Equation of Continuity
• Torricelli's Law

Thermal Properties of Matter

• Heat and Temperature
• Measurement of Temperature
• Ideal-gas 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 Black Body Radiation
• Wien's Displacement Law
• Stefan's Law
• Anomalous Expansion of Water
• Liquids and Gases
• Thermal Expansion of Solids
• Green House Effect

Thermodynamics

Kinetic Theory

• Molecular Nature of Matter
• Gases and Its Characteristics
• Equation of State of a Perfect Gas
• Work Done in Compressing a Gas
• Introduction of Kinetic Theory of an Ideal Gas
• Interpretation of Temperature in Kinetic Theory
• Law of Equipartition of Energy
• Specific Heat Capacities - Gases
• Mean Free Path
• Kinetic Theory of Gases - Concept of Pressure
• Assumptions of Kinetic Theory of Gases
• RMS Speed of Gas Molecules
• Degrees of Freedom
• Avogadro's Number

Oscillations

• Periodic and Oscillatory Motion
• Simple Harmonic Motion (S.H.M.)
• 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

• Reflection of Transverse and Longitudinal Waves
• Displacement Relation for a Progressive Wave
• The Speed of a Travelling Wave
• Principle of Superposition of Waves
• Introduction of Reflection of Waves
• Standing Waves and Normal Modes
• Beats
• Doppler Effect
• Wave Motion
• Speed of Wave Motion