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 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 Straight Line
Kinematics
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
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 and Its Characteristics
- 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 of Motion in One Dimension
Work, Energy and Power
- Introduction of Work, Energy and Power
- Notions of Work and Kinetic Energy: the Work-energy Theorem
- Kinetic Energy (K)
- Work Done by a Constant Force and a Variable Force
- Concept of Work
- Potential Energy (U)
- Conservation of Mechanical Energy
- Potential Energy of a Spring
- Various Forms of Energy : the Law of Conservation of Energy
- Power
- 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 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
Gravitation
- Kepler’s Laws
- Newton’s Universal Law of Gravitation
- The Gravitational Constant
- Acceleration Due to Gravity of the Earth
- Acceleration Due to Gravity Below and Above the Earth's Surface
- 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 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
- Poisson’s Ratio
Thermodynamics
Behaviour of Perfect Gases and Kinetic Theory of Gases
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
Oscillations and Waves
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
- 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 Process
- Heat Engine
- Refrigerators and Heat Pumps
- Second Law of Thermodynamics
- Reversible and Irreversible Processes
- Carnot Engine
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
- Simple Pendulum
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
- Variation of g with altitude
- Variation of g with depth
- Graph of g, R and d
Notes
Acceleration due to gravity below the surface of earth
- To calculate acceleration due to gravity below the surface of the earth (between the surface and centre of the earth).
Density of the earth is constant throughout. Therefore,
ρ = Me / (4/3π Re3) ....(1)
where,
Me = mass of the earth
Volume of sphere= `4/3π "R"_e^2`
Re = radius of the earth.
As entire mass is concentrated at the centre of the earth.
Therefore density can be written as
`rho = M_s(4/3π "R"_s^3)` ....(2)
Comparing equation (1) and (2)
`"M"_e/"M"_s="R"_e^3/"R"_s^3 "where" "R"_s= ("R"_e-"d")^3`
d= distance of the body form the centre to the surface of the earth.
Therefore,
`"M"_e/"M"_s="R"_e^3/("R"_e-"d")^3`
`"M"_s = "M"_e(("R"_e-"d")^3)/"R"_e^3` ...(3)
To calculate Gravitational force (F) between earth and point mass m at a depth d below the surface of the earth.
Above figure shows the value of g at a depth d. In this case only the smaller sphere of radius `("R"_e- "d")` contributes to g.
`"F" ="GmM"_s/("R"_e-"d")^2`
`"g"="F"/"m"` where g=acceleration due to gravity at point 'd' below the surface of the earth.
`"g"="GM"_s/("R"_e-"d")^2`
Putting the value of `"M"_s` from Eq.(3)
`="GM"_e("R"_e-"d")^3/("R"_e^3("R"_e-"d")^2)`
`="GM"_e(R_e-d)/R_e^3`
W.k.t. `"g"="GM"_e/"R"_e^2`
`g(d)="GM"_e/R_e^3("R"_e-"d")`
`=g((R_e-d)/R_e)=g(1-d/R_e)`
Acceleration due to gravity above the surface of the earth:
-
To calculate the value of acceleration due to gravity of a point mass m at a height h above the surface of the earth.
-
Force of gravitation between the object and the earth will be
`F(h)=("GM"_Em)/(R_E + h)^2`
The acceleration experienced by the point mass is `("F"("h"))/"m"≡"g"("h")`
`"g"(h)=("F"(h))/m="GM"_E/("R"_E + h)^2` ...(1)
This is cleary less than the value of g on the surface of earth: `"g"="GM"_E/"R"_E^2` for h<<RE, we can expand the RHS of Eq.(1)
`g(h)="GM"_E/(R_E^2 (1+h/R_E)^2)`
`=g(1+h/"R"_E)^-2`
For `"h"/"R"_E`<<1. Using binomial expression,
`"g"(h)cong"g"(1-(2h)/R_E)`
Conclusion: The value of acceleration due to gravity varies on the surface, above surface and below the surface of the earth.
