——— 📏 Units & Measurements ———

——— 📐 SI Units ———

~ 📝 Definition ~

The International System of Units (SI) is the standard system used worldwide for measuring physical quantities.

• It is based on seven base units, such as meter (m) for length, kilogram (kg) for mass, and second (s) for time.
• Derived units are combinations of base units, e.g., m/s for speed.
• SI units ensure consistency and universal understanding in science and engineering.

——— ↔️ Scalars vs. Vectors ———

~ 🔍 Overview ~

Physical quantities can be classified as scalars or vectors.

• Scalars: Quantities with only magnitude (size or amount). Examples: temperature, mass, time, distance.
• Vectors: Quantities with both magnitude and direction. Examples: velocity, force, displacement, acceleration.

~ 🎯 Key Properties ~

• Vectors are usually represented with arrows or boldface letters, e.g., \(\vec{v}\).
• Vector addition follows geometric rules (triangle or parallelogram law).
• Scalar operations are simple arithmetic (addition, subtraction).

——— 🧮 Dimensional Analysis ———

~ 📊 Purpose ~

Dimensional analysis helps check the correctness of physical equations by comparing the dimensions on both sides.

~ 🛠️ How it Works ~

• Every physical quantity can be expressed in terms of fundamental dimensions: Mass \([M]\), Length \([L]\), Time \([T]\), etc.
• For example, velocity has dimensions \([L T^{-1}]\), acceleration \([L T^{-2}]\).
• Equations are dimensionally consistent if both sides have the same dimensional formula.

~ 🔑 Benefits ~

• Detects errors in formulas or calculations.
• Helps derive relationships between physical quantities.
• Assists in unit conversions and scaling laws.