Quantities with Dimensions and Type
| Physical Quantity | Dimension | Scalar / Vector |
|---|---|---|
| Length | [L] | Scalar |
| Mass | [M] | Scalar |
| Time | [T] | Scalar |
| Velocity | [LT⁻¹] | Vector |
| Acceleration | [LT⁻²] | Vector |
| Force (F = ma) | [MLT⁻²] | Vector |
| Work (W = F·d) | [ML²T⁻²] | Scalar |
| Power (P = W/t) | [ML²T⁻³] | Scalar |
| Momentum (p = mv) | [MLT⁻¹] | Vector |
| Pressure (P = F/A) | [ML⁻¹T⁻²] | Scalar |
| Density (ρ = m/V) | [ML⁻³] | Scalar |
| Energy | [ML²T⁻²] | Scalar |
| Displacement | [L] | Vector |
| Angular Velocity | [T⁻¹] | Vector |
| Torque | [ML²T⁻²] | Vector |
General Quantities
| Quantity | Dimension | Scalar / Vector |
|---|---|---|
| Angular Velocity (rad/s) | [T⁻¹] | Vector |
| Angular Acceleration (rad/s²) | [T⁻²] | Vector |
| Moment of Inertia (kg·m²) | [ML²] | Scalar |
Thermodynamics
| Quantity | Dimension | Scalar / Vector |
|---|---|---|
| Heat (J) | [ML²T⁻²] | Scalar |
| Specific Heat Capacity (J/kg·K) | [L²T⁻²Θ⁻¹] | Scalar |
| Entropy (J/K) | [ML²T⁻²Θ⁻¹] | Scalar |
| Thermal Conductivity (W/m·K) | [MLT⁻³Θ⁻¹] | Scalar |
Electromagnetism
| Quantity | Dimension | Scalar / Vector |
|---|---|---|
| Electric Charge (C = A·s) | [TI] | Scalar |
| Electric Potential (V = J/C) | [ML²T⁻³I⁻¹] | Scalar |
| Electric Field Strength (N/C or V/m) | [MLT⁻³I⁻¹] | Vector |
| Capacitance (F = C/V) | [M⁻¹L⁻²T⁴I²] | Scalar |
| Resistance (Ω = V/A) | [ML²T⁻³I⁻²] | Scalar |
| Conductance (S = 1/Ω) | [M⁻¹L⁻²T³I²] | Scalar |
| Magnetic Flux (Wb = V·s) | [ML²T⁻²I⁻¹] | Scalar |
| Magnetic Flux Density (T = Wb/m²) | [MT⁻²I⁻¹] | Vector |
| Inductance (H = Wb/A) | [ML²T⁻²I⁻²] | Scalar |
Waves & Optics
| Quantity | Dimension | Scalar / Vector |
|---|---|---|
| Frequency (Hz = 1/s) | [T⁻¹] | Scalar |
| Wavelength (m) | [L] | Scalar |
| Wave Speed (m/s) | [LT⁻¹] | Scalar |
| Intensity (W/m²) | [MT⁻³] | Scalar |
| Refractive Index | Dimensionless | Scalar |
Modern Physics
| Quantity | Dimension | Scalar / Vector |
|---|---|---|
| Planck’s Constant (J·s) | [ML²T⁻¹] | Scalar |
| Electric Dipole Moment (C·m) | [LTI] | Vector |
| Activity (Bq = 1/s) | [T⁻¹] | Scalar |
Supplementary Quantities
| Quantity | Dimension | Scalar / Vector |
|---|---|---|
| Plane Angle (radian) | Dimensionless | Scalar |
| Solid Angle (steradian) | Dimensionless | Scalar |
Other Important Quantities
| Quantity | Dimension | Scalar / Vector |
|---|---|---|
| Viscosity (Pa·s) | [ML⁻¹T⁻¹] | Scalar |
| Surface Tension (N/m) | [MT⁻²] | Scalar |
| Gravitational Constant (G) | [M⁻¹L³T⁻²] | Scalar |
| Boltzmann Constant (k) | [ML²T⁻²Θ⁻¹] | Scalar |
| Permittivity of Free Space (ε₀) | [M⁻¹L⁻³T⁴I²] | Scalar |
| Permeability of Free Space (μ₀) | [MLT⁻²I⁻²] | Scalar |
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