Physics Equations
Physics Equations
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: \(N = 368\) |