Dimensional Analysis Lecture Notes

A set of flashcards covering the dimensions (M, L, T) of various physical quantities based on lecture notes.

Length Terms (Radius of Gyration, Astronomical unit, parsec, light year)

All these terms have the dimension $[L]$.

Velocities (General)

Standard velocities have the dimension $[LT^{-1}]$.

Angular velocity

This specific velocity has the dimension $[T^{-1}]$.

Acceleration (General)

Standard acceleration has the dimension $[LT^{-2}]$.

Angular acceleration

This specific acceleration has the dimension $[T^{-2}]$.

Force Terms (Thrust, Viscous drag, normal reaction, tension, Weight)

All these expressions of force have the dimensions $[MLT^{-2}]$.

Surface tension and Spring Constant

These terms share the dimension $[MT^{-2}]$.

Work, Energies, Torque, Couple, and Moment of force

These quantities have the dimensions $[ML^2T^{-2}]$.

Pressure and Stress

These terms have the dimensions $[ML^{-1}T^{-2}]$.

Modulus Terms (Young, Bulk, Sheer, Modulus of rigidity)

All these terms share the same dimensions as pressure ($[ML^{-1}T^{-2}]$).

Gradient terms

Calculated as the derived quantity divided by length ($\frac{\text{derived}}{\text{Length}}$).

Momentum and Impulse

Both of these quantities have the same dimensions of $[MLT^{-1}]$.

Angular momentum

Defined as Momentum $\times$ distance, with dimensions $[ML^2T^{-1}]$.

Linear density

Dimensions defined as $[ML^{-1}]$.

Areal charge

Dimensions defined as $[ML^{-2}]$.

Volumetric density

Dimensions defined as $[ML^{-3}]$.