Physics Lectures PDF

# Unit 1: Measurement ## 1.1 Introduction * **Physical quantities** can be measured and are expressed numerically. * A complete set of units for all physical quantities is called a **system of units**. ## 1.2 Units and Systems of Units * **Base quantities**: a few quantities which are used to defin...

# Unit 1: Measurement ## 1.1 Introduction * **Physical quantities** can be measured and are expressed numerically. * A complete set of units for all physical quantities is called a **system of units**. ## 1.2 Units and Systems of Units * **Base quantities**: a few quantities which are used to define all other quantities. * **Base units**: units for base quantities. * **Derived quantities**: quantities expressed in terms of base quantities. * **Derived units**: units for derived quantities. * **SI (Systeme International)** is the accepted system of units for the whole world. * **SI base units**: | Base Quantity | Symbol | SI Base Unit | Symbol | |---|---|---|---| | Length | l,x,r e.t.c | Meter | m | | Mass | m | Kilogram | kg | | Time | t | Second | s | | Electric current | I | Ampere | A | | Thermodynamic temperature | T | Kelvin | K | | Amount of substance | n | Mole | mol | | Luminous intensity | I | Candela | cd | * **Derived Units**: Derived quantities are a combination of base quantities and their units - for example: * Area is length x length and the unit: $m^2$ * Volume is: $m^3$ * **Supplementary Units**: * **Radian (rad)**: the angle subtended at the center of a circle by an arc with a length equal to the radius of the circle * **Steradian (sr)**: The solid angle subtended at the center of a sphere by an area of its surface equal to the square of the radius. * **The most natural way to measure an angle is not in degrees, but in radians** ## 1.3 Scientific Notation: * Scientific notation is used to express very large or very small numbers. * **Number = Mantissa × 10^Exponent** * **Advantages**: * Concise way of expressing large/small numbers * Easy to perform calculations like addition, subtraction, multiplication, and division of large/small numbers ## 1.4 Significant Figures: * **Precision**: Closeness of measurements to each other * **Accuracy**: Closeness of measurements to the actual value of the quantity * **Significant figures**: Digits of a number that are considered reliable * **Rules for significant figures**: * Non-zero digits are always significant. 1234 has four significant figures * Zeros between non-zero digits are always significant. 10203 has five significant figures. * Zeros to the left of the first non-zero digit are not significant. 0.001 has one significant figure, 0.012 has two significant figures. * Zeros to the right of the last non-zero digit are significant if there is a decimal point in the number. 1.200 has four significant figures. * **In a calculation involving addition or subtraction, the result should contain the same number of decimal places as the number with the fewest decimal places.** * **In a calculation involving multiplication or division, the result should contain the same number of significant figures as the number with the fewest significant figures.** ## 1.5 Errors in Measurements: * **Error**: The difference between the measured value and the true value of the quantity. * **Different types of errors**: * **Systematic errors**: Errors that tend to be in one direction, either positive or negative. * **Instrumental errors**: Caused by faulty instruments. * **Personal errors**: Caused by the observer's carelessness or bias. * **Random errors**: Errors that occur irregularly and are unpredictable. * **Least count**: the smallest value that can be measured by a measuring instrument * **Least count error**: the error associated with the resolution of the measuring instrument. It is usually a random error. ## 1.6 Uncertainty: * **Uncertainty**: It is the quantification of the doubt in a measurement. * **Types of uncertainty**: * **Absolute uncertainty**: The same unit as the quantity. Denoted by **Delta**. * **Relative uncertainty**: No units. Denoted by **epsilon**. ## 1.7. Addition of Uncertainties: * **Sum or difference**: Absolute uncertainties are added. * **Product or quotient**: Fractional uncertainties are converted into percentage uncertainties, which are then added. * **Power**: The percentage uncertainty is multiplied by the power, and then converted back to fractional uncertainty. ## 1.8: Dimensions of Physical Quantities: * **Dimensions**: Used to describe the physical nature of a quantity. * **Dimensional Formula**: Shows how and which base quantities represent the dimensions of a physical quantity. * **Dimensional Equation**: Equates a physical quantity with its dimensional formula * **Uses of dimensional analysis**: * To check the correctness of a physical equation or its derivation. * To derive a possible formula for a physical quantity ## 1.9: Dimensional Constants and Variables: * **Dimensional Constants**: Have dimensions and are constant * Speed of Light * Gravitational constant * Plank's constant * **Dimensional Variables**: Have dimensions and are variable. * Force * Energy * Acceleration * **Dimensionless constants**: No dimensions and are constant. * Pure numbers * The number π ## 1.10: Dimensionless Variables: * **Dimensionless Variables**: No dimensions and are variable * Plane angle * Solid angle * Strain