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 Non-Uniform Motion
- Uniformly Accelerated Motion
- Position-time, Velocity-time and Acceleration-time Graphs
- Motion in a Straight Line - Position-time 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 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
Work, Energy and Power
- Introduction of Work, Energy and Power
- Notions of Work and Kinetic Energy: the Work-Energy 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
- 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
- Newton’s 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
- Thrust and Pressure
- Transmission of Pressure in Liquids: Pascal’s Law
- Variation of Pressure with Depth
- Atmospheric Pressure and Gauge Pressure
- Hydraulic Machines
- STREAMLINE FLOW
- Applications of Bernoulli’s Equation
- Viscous Force Or 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
- 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 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 Process
- 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
- 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
- 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 (SHM)
- 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
description
- Measurement of Large Distances - parallax angle or parallactic angle
- Estimation of Very Small Distances : Size of a Molecule
- Range of Lengths
notes
Measurement of Length
Length can be measured using metre scale (10-3m to 102m), vernier callipers (10-4 m) and screw gauge and spherometer (10-5 m).
Measurement of Large Distances
Large distances such as the distance of a planet or a star from the earth cannot be measured directly with a metre scale. An important method in such cases is the parallax method.
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. Distance between the two viewpoints is called Basis.
When you hold a pencil in front of you against some specific point on the background (a wall) and look at the pencil first through your left eye A (closing the right eye) and then look at the pencil through your right eye B (closing the left eye), you would notice that the position of the pencil seems to change with respect to the point on the wall. This is called parallax. The distance between the two points of observation is called the basis. In this example, the basis is the distance between the eyes.
Measuring distance of a planet using parallax method
Measuring the distance of a far away planet:
Let us assume S is a planet a distance D from earth. A and B are two observatories on earth.
Distance AB = b
Parallax Angle ∠ASB = θ
As the planet is very far away.
So, `b/D`<< 1
and hence, θ is very small.
AB is an arc of circle with centre S and radius D
D = AS = BS
AB = b = Dθ, where θ is in radians
D = `b/θ` ....(i)
After determining D, size or angular diameter at the planet can be determined using same method.
α = `d/D` ....(ii)
Using these two equations, diameter of planet can be calculated.
Measuring very small distances
-To measure distances as low as size of a molecule, electron microscopes are used. These contain electrons beams controlled by electric and magnetic fields.
- Electron microscopes have a resolution of 0.6 Å or Angstroms.
- Electron microscopes are able to resolve atoms and molecules while using tunneling microscopy, it is possible to estimate size of molecule.
Estimating size of molecule of Oleic acid :-
The steps followed in determining the size of molecule are:
-
Dissolve 1 cm3 of oleic acid in alcohol to make a solution of 20 cm3.Take 1 cm3 of above solution and dissolve in alcohol to make a solution of 20 cm3 Concentration of oleic acid in the solution will be (1/(20x20)) cm3.
-
Sprinkle lycopodium powder on the surface of water in a trough and put one drop of above solution. The oleic acid in the solution will spread over water in a circular molecular thick film.
-
Measure the diameter of the above circular film using below calculations.
-
If n – Number of drops of solution in water, V – Volume of each drop, t – Thickness of the film, A – Area of the film
Total volume of n drops of solution = nV cm3
Amount of Oleic acid in this solution = nV(1/(20 x 20)) cm3
Thickness of the film t = Volume of the film / Area of the film
t = nV/(20x20A) cm
Range of Lengths
The sizes of the objects we come across in the universe vary over a very wide range. These may vary from the size of the order of 10–14 m of the tiny nucleus of an atom to the size of the order of 1026 m of the extent of the observable universe. Table below gives the range and order of lengths and sizes of some of these objects
Size of object or distance | Length (m) |
Size of a proton | 10-15 |
Size of atomic nucleus | 10-14 |
size of hydrogen atom | 10-10 |
Length of typical virus | 10-8 |
Wavelength of light | 10-7 |
Size of red blood corpuscle | 10-5 |
Thickness of a paper | 10-4 |
Height of the Mount Everest above sea level | 104 |
Radius of the Earth | 107 |
Distance of the moon from the Earth | 108 |
Distance of the Sun from the Earth | 1011 |
Distance of Pluto from the Sun | 1013 |
Size of galaxy | 1021 |
Distance to Andromeda galaxy | 1022 |
Distance to the boundary of observable universe | 1026 |