Physics Equations

Physics Equations
Author

Benedict Thekkel

1. Mechanics (Motion, Forces, and Energy)

1.1 Kinematics (Motion)

Describes the motion of objects without considering forces.

Equation Description Example
\(v = u + at\) Final velocity (\(v\)) after time (\(t\)) with acceleration (\(a\)) A car accelerates from 10 m/s at 2 m/s² for 5 s. Find \(v\).
\(v = 10 + (2 \times 5) = 20\) m/s
\(s = ut + \frac{1}{2}at^2\) Displacement (\(s\)) after time \(t\) A ball drops from rest under gravity for 3 s. Find \(s\).
\(s = 0 + \frac{1}{2}(9.8)(3)^2 = 44.1\) m
\(v^2 = u^2 + 2as\) Final velocity squared A car starts at 5 m/s, accelerates at 3 m/s², and moves 20 m. Find \(v\).
\(v^2 = 5^2 + 2(3)(20) = 125\), \(v = 11.18\) m/s

1.2 Newton’s Laws of Motion

Describes how forces affect motion.

Equation Description Example
\(F = ma\) Force (\(F\)) is mass (\(m\)) times acceleration (\(a\)) A 10 kg object accelerates at 5 m/s². Find \(F\).
\(F = 10 \times 5 = 50\) N
\(p = mv\) Momentum (\(p\)) is mass times velocity A 2 kg ball moving at 4 m/s has momentum \(2 \times 4 = 8\) kg·m/s
\(F \Delta t = m \Delta v\) Impulse is force times time A 0.5 kg ball hits a wall and bounces back with the same speed of 10 m/s. Force applied for 0.2 s is \(F = (0.5 \times 20)/0.2 = 50\) N

1.3 Work, Energy, and Power

Equation Description Example
\(W = Fd \cos \theta\) Work done by force \(F\) over displacement \(d\) A force of 50 N moves an object 10 m at an angle of 30°. \(W = 50 \times 10 \times \cos 30° = 433\) J
\(KE = \frac{1}{2} mv^2\) Kinetic energy A 3 kg object moving at 5 m/s has \(KE = 37.5\) J
\(PE = mgh\) Gravitational potential energy A 2 kg object at 5 m has \(PE = 2 \times 9.8 \times 5 = 98\) J
\(P = \frac{W}{t}\) Power is work per time A machine does 1000 J in 2 s. Power is \(500\) W

2. Electricity and Magnetism

2.1 Electric Circuits

Equation Description Example
\(V = IR\) Ohm’s Law (Voltage, Current, Resistance) A 10Ω resistor with 5A current has \(V = 10 \times 5 = 50V\)
\(P = VI\) Power in an electric circuit A 230V appliance draws 2A. Power is \(460W\)
\(Q = It\) Charge is current times time A 2A current flows for 5s. Charge is \(10C\)

2.2 Magnetism

Equation Description Example
\(F = BIL \sin \theta\) Force on a wire in a magnetic field A 2m wire with 3A in a 0.5T field at 90° has \(F = 3N\)
\(\Phi = B A \cos \theta\) Magnetic flux A 0.1m² loop in a 2T field at 90° has \(\Phi = 0.2\) Wb

3. Electromagnetic Waves & Optics

3.1 Wave Equations

Equation Description Example
\(v = f\lambda\) Wave speed A 500Hz sound wave in air (\(v = 340\) m/s) has \(\lambda = 0.68\) m
\(I = \frac{P}{A}\) Intensity of a wave A 100W light source emitting over 10m² has \(I = 10\) W/m²

3.2 Optics (Reflection & Refraction)

Equation Description Example
\(n_1 \sin \theta_1 = n_2 \sin \theta_2\) Snell’s Law Light moving from air (\(n = 1.0\)) to water (\(n = 1.33\)) at 30° bends at \(\theta_2 = 22°\)

4. Thermodynamics

Equation Description Example
\(Q = mc\Delta T\) Heat energy change Heating 1 kg of water by 10°C takes \(Q = 4184 \times 1 \times 10 = 41.84\) kJ
\(PV = nRT\) Ideal gas law A gas at 300K with \(2\) moles in 0.1m³ has \(P = 4.92\) kPa

5. Relativity

Equation Description Example
\(E = mc^2\) Energy-mass equivalence 1kg of mass converts to \(9 \times 10^{16}\) J

6. Quantum Physics

Equation Description Example
\(E = hf\) Photon energy A 500 THz photon has energy \(3.32 \times 10^{-19}\) J

7. Nuclear Physics

Equation Description Example
\(N = N_0 e^{-\lambda t}\) Radioactive decay If \(\lambda = 0.1\) and \(N_0 = 1000\), after 10s: \(N = 368\)
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