Units of Measurement and Fundamental Units#

Measurement in Physics#

Measurement is the process of comparing an unknown quantity with a known standard quantity. The result of a measurement is expressed as a numerical value along with appropriate units.

Fundamental Units (Base Units)#

The International System of Units (SI) defines seven fundamental units:

1. Meter (m) - Unit of length
2. Kilogram (kg) - Unit of mass
3. Second (s) - Unit of time
4. Ampere (A) - Unit of electric current
5. Kelvin (K) - Unit of thermodynamic temperature
6. Mole (mol) - Unit of amount of substance
7. Candela (cd) - Unit of luminous intensity

Derived Units#

Derived units are formed by combining fundamental units through multiplication or division. Common examples include:

• Newton (N) = kg·m/s² (Force)
• Joule (J) = kg·m²/s² (Energy)
• Watt (W) = kg·m²/s³ (Power)
• Pascal (Pa) = N/m² (Pressure)
• Coulomb (C) = A·s (Electric charge)

SI Prefixes#

Standard prefixes used to denote powers of 10:

• Tera (T) = 10¹²
• Giga (G) = 10⁹
• Mega (M) = 10⁶
• Kilo (k) = 10³
• Centi (c) = 10⁻²
• Milli (m) = 10⁻³
• Micro (μ) = 10⁻⁶
• Nano (n) = 10⁻⁹
• Pico (p) = 10⁻¹²

Important Constants#

• Speed of light in vacuum: c = 3.00 × 10⁸ m/s
• Gravitational constant: G = 6.674 × 10⁻¹¹ N·m²/kg²
• Planck’s constant: h = 6.626 × 10⁻³⁴ J·s
• Elementary charge: e = 1.602 × 10⁻¹⁹ C

Significant Figures#

The number of significant figures in a measurement indicates the precision of the measurement. Rules for significant figures:

1. All non-zero digits are significant
2. Zeros between non-zero digits are significant
3. Leading zeros are not significant
4. Trailing zeros in a decimal are significant
5. Trailing zeros in a whole number may or may not be significant

Dimensional Analysis#

Dimensional analysis is a method to check the consistency of equations and derive relationships between physical quantities. Each physical quantity can be expressed in terms of fundamental dimensions [M], [L], and [T].