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Physics is the branch of science that studies matter, energy, motion, and the fundamental forces of nature. It seeks to explain how the universe behaves from subatomic particles to galaxies.

Below is a structured overview of major areas of physics and their key formulas (with short explanations).

1. Mechanics (Motion & Forces)

Kinematics (Describing Motion)

• Displacement: $$s = vt$$ (constant velocity)
• Uniform acceleration:
  • $$v = u + at$$
  • $$s = ut + tfrac{1}{2}at^2$$
  • $$v^2 = u^2 + 2as$$
    Where:
• u = initial velocity
• v = final velocity
• a = acceleration
• s = displacement
• t = time

Dynamics (Causes of Motion)

• Newtons Second Law: $$F = ma$$
• Weight: $$W = mg$$
• Momentum: $$p = mv$$
• Impulse: $$F Delta t = Delta p$$

Energy & Work

• Work: $$W = Fdcostheta$$
• Kinetic Energy: $$E_k = tfrac{1}{2}mv^2$$
• Potential Energy: $$E_p = mgh$$
• Power: $$P = tfrac{W}{t}$$

Circular Motion

• Centripetal Force: $$F = tfrac{mv^2}{r}$$
• Centripetal Acceleration: $$a = tfrac{v^2}{r}$$

2. Thermodynamics (Heat & Energy)

• Heat: $$Q = mcDelta T$$
• First Law of Thermodynamics: $$Delta U = Q – W$$
• Ideal Gas Law: $$PV = nRT$$
• Efficiency: $$eta = tfrac{W_{out}}{Q_{in}} times 100%$$

3. Waves and Oscillations

• Wave Speed: $$v = flambda$$
• Period and Frequency: $$f = tfrac{1}{T}$$
• Simple Harmonic Motion: $$x = Asin(omega t + phi)$$
• Angular Frequency: $$omega = 2pi f$$

4. Electricity and Magnetism

• Ohms Law: $$V = IR$$
• Power in Circuits: $$P = VI = I^2R = tfrac{V^2}{R}$$
• Coulombs Law: $$F = k tfrac{q_1 q_2}{r^2}$$
• Electric Field: $$E = tfrac{F}{q}$$
• Potential Difference: $$V = Ed$$
• Magnetic Force: $$F = qvBsintheta$$
• Faradays Law: $$text{EMF} = -N tfrac{dPhi}{dt}$$

5. Light and Optics

• Snells Law: $$n_1 sintheta_1 = n_2 sintheta_2$$
• Lens/Mirror Formula: $$tfrac{1}{f} = tfrac{1}{u} + tfrac{1}{v}$$
• Magnification: $$m = tfrac{h_i}{h_o} = -tfrac{v}{u}$$

6. Modern Physics

Relativity

• MassEnergy Equivalence: $$E = mc^2$$
• Time Dilation: $$t’ = tfrac{t}{sqrt{1 – v^2/c^2}}$$

Quantum Physics

• Photon Energy: $$E = hf$$
• de Broglie Wavelength: $$lambda = tfrac{h}{p}$$
• Heisenberg Uncertainty Principle: $$Delta x, Delta p ge tfrac{h}{4pi}$$

Nuclear Physics

• Radioactive Decay: $$N = N_0 e^{-lambda t}$$
• Half-life: $$t_{1/2} = tfrac{0.693}{lambda}$$

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