Physics¶

The laws of the universe, derived from first principles.

Mechanics¶

Newton's Laws - The definitions of motion (\(F=ma\)).
Centripetal Acceleration - Deriving \(a_c = \frac{v^2}{r}\) from geometric analysis.
Simple Harmonic Motion - Deriving the period formula \(T = 2\pi\sqrt{\frac{m}{k}}\).
Kinetic Energy - Deriving \(K = \frac{1}{2}mv^2\) from the definition of Work.
Gravitational Potential Energy - Deriving \(U = mgh\) and why lifting things makes you tired.

Coulomb's Law - Why electric force is inversely proportional to distance squared.

Measuring the Universe - How we weighed the Earth (\(G\)) and measured gravity (\(g\)) without satellites.

Schrödinger Equation - The fundamental equation of quantum mechanics (\(i\hbar \frac{\partial}{\partial t} \Psi = \hat{H} \Psi\)).
Heisenberg Uncertainty Principle - Fundamental limits on measurement precision (\(\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\)).
Rabi Frequency - Quantum oscillations between energy levels (\(\Omega_R = |\mathbf{d} \cdot \mathbf{E}_0|/\hbar\)).
Born Rule - The probabilistic interpretation of the wave function (\(P = |\langle \phi | \Psi \rangle|^2\)).

Doppler Effect - Why pitch and color shift with motion (\(f = f_0 \frac{v + v_o}{v - v_s}\)).