Units and Measurements

Physics is the study of matter and its interaction with energy. The major branches of physics include Mechanics, Light, Electricity, Waves, Magnetism, Atomic Physics, Electromagnetism, Dynamics, Heat, and Sound.

Matter

Matter is anything that has mass and occupies space. The concept that matter is made up of tiny particles called atoms dates back to ancient Greece. An atom is the smallest indivisible unit of an element that participates in chemical reactions. It consists of:

Matter exists in three states:

  1. Solid: Molecules are tightly packed, giving solids a definite shape and volume.
  2. Liquid: Molecules move more freely than in solids. Liquids have a definite volume but no fixed shape.
  3. Gas: Molecules move independently, with negligible forces binding them. Gases have neither a fixed shape nor a definite volume.

Quantities and Units

Physical quantities are classified into two types:

  1. Fundamental Quantities: Basic physical quantities that are independent and cannot be derived from others. Examples include:
    • Mass - Kilogram (kg)
    • Length - Meter (m)
    • Time - Second (s)
    • Temperature - Kelvin (K)
    • Electric Current - Ampere (A)
    • Luminous Intensity - Candela (cd)
    • Amount of Substance - Mole (mol)
  2. Derived Quantities: These are obtained from fundamental quantities. Examples include:
    • Area - \( m^2 \)
    • Volume - \( m^3 \)
    • Density - \( kg/m^3 \)
    • Velocity - \( m/s \)
    • Force - \( N = kg \cdot m/s^2 \)
    • Power - \( W = J/s \)
    • Pressure - \( Pa = N/m^2 \)

Position, Distance, and Displacement

Position: The specific location of an object in space relative to a reference point.

Distance: The separation between two points. If two points in a plane are represented as \((x_1, y_1)\) and \((x_2, y_2)\), the distance between them is given by:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

In three-dimensional space, with coordinates \((x_1, y_1, z_1)\) and \((x_2, y_2, z_2)\), the formula extends to:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} $$

Displacement: The shortest distance between two points in a specified direction.

Measurement of Distance

Vernier Calipers

A vernier caliper is used to measure small lengths, such as the diameter of a rod or the internal/external diameter of a tube. It consists of two sets of jaws and two scales (main and vernier scale) and has an accuracy of 0.01 cm.

Vernier Calliper diagram Credit: Tumisang Laurel Kalagobe on Researchgate

Micrometer Screw Gauge

A micrometer screw gauge measures very small lengths, such as the diameter of a small ball or the thickness of a paper. It has an accuracy of 0.001 cm (or 0.01 mm).

Micrometer Screw gauge Credit: Brians Chinonso Amadi on Researchgate

Meter Rule

A meter rule is marked in centimeters and millimeters, with the smallest graduation being 1 mm (0.01 m). Longer distances, like the length of a football field, can be measured using steel tapes marked in meters.

Mass and Weight

Mass: The quantity of matter in an object, measured in kilograms (kg).

Weight: The force exerted on a mass due to gravity, measured in Newtons (N).

Common instruments for measuring mass:

Weight is typically measured using a spring balance.

Measurement of Time

Time is the duration of an event and is measured in seconds (s). Time measurement is based on oscillatory motion.

Instruments used for measuring time:

Dimensional Analysis

The dimension of a physical quantity expresses how it is related to fundamental units. For example, length is represented as \( L \), time as \( T \), and mass as \( M \).

Example: Velocity

Velocity is defined as:

$$ Velocity = \frac{Distance}{Time} $$

Since distance has the dimension \( L \) and time has \( T \), we get:

$$ Velocity = \frac{L}{T} = LT^{-1} $$