Fundamental Theorems & Formulas

A curated collection of essential principles in Classical Mechanics, Thermodynamics, and Stoichiometry. These resources are optimized for quick reference during laboratory sessions.

Physics: Classical Mechanics

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it.

Newton's Second Law

$$ F_{net} = m \cdot a $$

Where F is the net force applied, m is the mass of the object, and a is the acceleration.

Kinematic Equations (Constant Acceleration)

$$ x = x_0 + v_0t + \frac{1}{2}at^2 $$

$$ v^2 = v_0^2 + 2a(x - x_0) $$

Work-Energy Theorem

$$ W_{net} = \Delta K = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2 $$

Chemistry: Stoichiometry & Gas Laws

Understanding the behavior of gases and the quantitative relationships in chemical reactions is crucial for advanced chemistry studies.

Ideal Gas Law

$$ PV = nRT $$

Describes the state of a hypothetical ideal gas. P is pressure, V is volume, n is amount of substance, R is the ideal gas constant, and T is absolute temperature.

Molarity Calculation

$$ M = \frac{n_{solute}}{V_{solution} (L)} $$

Applied Mathematics

Quadratic Formula

$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

Euler's Identity

$$ e^{i\pi} + 1 = 0 $$

Often cited as the most beautiful equation in mathematics.