Topics
Units and Measurements
 Introduction of Units and Measurements
 System of Units
 Measurement of Length
 Measurement of Mass
 Measurement of Time
 Dimensions and Dimensional Analysis
 Accuracy, Precision and Uncertainty in Measurement
 Errors in Measurements
 Significant Figures
Mathematical Methods
 Vector Analysis
 Vector Operations
 Resolution of Vectors
 Multiplication of Vectors
 Introduction to Calculus
Motion in a Plane
 Introduction to Motion in a Plane
 Rectilinear Motion
 Motion in Two DimensionsMotion in a Plane
 Uniform Circular Motion (UCM)
Laws of Motion
 Introduction to Laws of Motion
 Aristotle’s Fallacy
 Newton’s Laws of Motion
 Inertial and Noninertial Frames of Reference
 Types of Forces
 Work Energy Theorem
 Principle of Conservation of Linear Momentum
 Collisions
 Impulse of Force
 Rotational Analogue of a Force  Moment of a Force Or Torque
 Couple and Its Torque
 Mechanical Equilibrium
 Centre of Mass
 Centre of Gravity
Gravitation
 Introduction to Gravitation
 Kepler’s Laws
 Newton’s Universal Law of Gravitation
 Measurement of the Gravitational Constant (G)
 Acceleration Due to Gravity (Earth’s Gravitational Acceleration)
 Variation in the Acceleration Due to Gravity with Altitude, Depth, Latitude and Shape
 Gravitational Potential and Potential Energy
 Earth Satellites
Mechanical Properties of Solids
 Introduction to Mechanical Properties of Solids
 Elastic Behavior of Solids
 Stress and Strain
 Hooke’s Law
 Elastic Modulus
 Stressstrain Curve
 Strain Energy
 Hardness
 Friction in Solids
Thermal Properties of Matter
 Introduction to Thermal Properties of Matter
 Heat and Temperature
 Measurement of Temperature
 Absolute Temperature and Ideal Gas Equation
 Thermal Expansion
 Specific Heat Capacity
 Calorimetry
 Change of State
 Heat Transfer
 Newton’s Law of Cooling
Sound
 Introduction to Sound
 Types of Waves
 Common Properties of All Waves
 Transverse Waves and Longitudinal Waves
 Mathematical Expression of a Wave
 The Speed of Travelling Waves
 Principle of Superposition of Waves
 Echo, Reverberation and Acoustics
 Qualities of Sound
 Doppler Effect
Optics
 Introduction to Ray Optics
 Nature of Light
 Ray Optics Or Geometrical Optics
 Reflection
 Refraction
 Total Internal Reflection
 Refraction at a Spherical Surface and Lenses
 Dispersion of Light and Prisms
 Some Natural Phenomena Due to Sunlight
 Defects of Lenses (Aberrations of Optical Images)
 Optical Instruments
 Optical Instruments: Simple Microscope
 Optical Instruments: Compound Microscope
 Optical Instruments: Telescope
Electrostatics
 Introduction to Electrostatics
 Electric Charges
 Basic Properties of Electric Charge
 Coulomb’s Law  Force Between Two Point Charges
 Principle of Superposition
 Electric Field
 Electric Flux
 Gauss’s Law
 Electric Dipole
 Continuous Distribution of Charges
Electric Current Through Conductors
 Electric Current
 Flow of Current Through a Conductor
 Drift Speed
 Ohm's Law (V = IR)
 Limitations of Ohm’s Law
 Electrical Power
 Resistors
 Specific Resistance (Resistivity)
 Variation of Resistance with Temperature
 Electromotive Force (emf)
 Combination of Cells in Series and in Parallel
 Types of Cells
 Combination of Resistors  Series and Parallel
Magnetism
 Introduction to Magnetism
 Magnetic Lines of Force and Magnetic Field
 The Bar Magnet
 Gauss' Law of Magnetism
 The Earth’s Magnetism
Electromagnetic Waves and Communication System
 EM Wave
 Electromagnetic Spectrum
 Propagation of EM Waves
 Introduction to Communication System
 Modulation
Semiconductors
 Introduction to Semiconductors
 Electrical Conduction in Solids
 Band Theory of Solids
 Intrinsic Semiconductor
 Extrinsic Semiconductor
 pn Junction
 A pn Junction Diode
 Semiconductor Devices
 Applications of Semiconductors and Pn Junction Diode
 Thermistor
 Order of magnitude
 Significant figures
 Addition and subtraction of significant figures
 Multiplication and division of significant figures
 Rules for limiting the result to the required number of significant figures
 Rules for arithmetic operations with significant figures
 Roundingoff in the measurement
Significant Figures
Every measurement results in a number that includes reliable digits and uncertain digits. Reliable digits plus the first uncertain digit are called significant digits or significant figures. These indicate the precision of measurement, which depends on the least count of measuring instruments.
A choice of change of different units does not change the number of significant digits or figures in a measurement.
For example, the period of oscillation of a pendulum is 1.62 s. Here, 1 and 6 are reliable, and 2 is uncertain. Thus, the measured value has three significant figures.
Rules for determining number of significant figures:

All nonzero digits are significant.

All zeros between two nonzero digits are significant, irrespective of decimal place.

For a value less than 1, zeroes after decimal and before nonzero digits are not significant. Zero before decimal place in such a number is always insignificant.
 Trailing zeroes in a number without decimal place are insignificant.
Cautions to remove ambiguities in determining number of significant figures

Change of units should not change number of significant digits. Example, 4.700m = 470.0 cm = 4700 mm. In this, the first two quantities have 4, but the third quantity has 2 significant figures.

Use scientific notation to report measurements. Numbers should be expressed in powers of 10 like a x 10b, where b is called order of magnitude. For example, 4.700 m = 4.700 x 102 cm = 4.700 x 103 mm = 4.700 x 103 In all the above, since the power of 10 is irrelevant, number of significant figures are 4.

Multiplying or dividing exact numbers can have infinite number of significant digits. For example, radius = diameter / 2. Here 2 can be written as 2, 2.0, 2.00, 2.000 and so on.
Rules for Arithmetic operation with Significant Figures
Type  Multiplication or Division  Addition or Subtraction 
Rule  The final result should retain as many significant figures as there in the original number with the lowest number of significant digits.  The final result should retain as many decimal places as there in the original number with the least decimal places. 
Example 
Density = Mass / Volume
if mass = 4.237 g (4 significant figures) and Volume = 2.51 cm^{3} (3 significant figures)
Density = 4.237 g/2.51 cm^{3} = 1.68804 g cm^{3} = 1.69 g cm^{3} (3 significant figures) 
Addition of 436.32 (2 digits after decimal), 227.2 (1 digit after decimal) & .301 (3 digits after decimal) is = 663.821
Since 227.2 is precise up to only 1 decimal place, Hence, the final result should be 663.8 
Rules for Rounding off the uncertain digits
Rounding off is necessary to reduce the number of insignificant figures to adhere to the rules of arithmetic operation with significant figures.
Rule Number  Insignificant Digit  Preceding Digit 
Example (rounding off to two decimal places) 
1  Insignificant digit to be dropped is more than 5  Preceding digit is raised by 1. 
Number – 3.137 Result – 3.14 
2  Insignificant digit to be dropped is less than 5  Preceding digit is left unchanged. 
Number – 3.132 Result – 3.13 
3  Insignificant digit to be dropped is equal to 5  If the preceding digit is even, it is left unchanged. 
Number – 3.125 Result – 3.12 
4  Insignificant digit to be dropped is equal to 5  If the preceding digit is odd, it is raised by 1. 
Number – 3.135 Result – 3.14 
Rules for determining uncertainty in results of arithmetic calculations
To calculate the uncertainty, the below process should be used.

Add the lowest amount of uncertainty in the original numbers. Example uncertainty for 3.2 will be ± 0.1, and for 3.22 will be ± 0.01. Calculate these in percentages also.

After the calculations, the uncertainties get multiplied/divided/added/subtracted.

Round off the decimal place in the uncertainty to get the final uncertainty result.
Example, for a rectangle, if length l = 16.2 cm and breadth b = 10.1 cm
Then, take l = 16.2 ± 0.1 cm or 16.2 cm ± 0.6% and breadth = 10.1 ± 0.1 cm or 10.1 cm ± 1%.
On Multiplication, area = length x breadth = 163.62 cm2 ± 1.6% or 163.62 ± 2.6 cm2.
Therefore, after rounding off, area = 164 ± 3 cm2.
Hence, 3 cm2 is the uncertainty or the error in estimation.
Rules:
1. For a set experimental data of ‘n’ significant figures, the result will be valid to ‘n’ significant figures or less (only in the case of subtraction).
Example 12.9  7.06 = 5.84 or 5.8 (rounding off to the lowest number of decimal places of the original number).
2. The relative error of a value of number specified to significant figures depends not only on n but also on the number itself.
For example, the accuracy for two numbers 1.02 and 9.89 is ±0.01. But relative errors will be:
For 1.02, (± 0.01/1.02) x 100% = ± 1%
For 9.89, (± 0.01/9.89) x 100% = ± 0.1%
Hence, the relative error depends upon number itself.
3. Intermediate results in multistep computation should be calculated to one more significant figure in every measurement than the number of digits in the least precise measurement.
Example:1/9.58 = 0.1044
Now, 1/0.104 = 9.56 and 1/0.1044 = 9.58
Hence, taking one extra digit gives more precise results and reduces roundingoff errors.