1st moment of area

under construction

Dimensional Analysis

Definition

mass: M
distance(Length): L
time: T
electric Charge: Q
temperature: Θ

speed = distance/time = L/T or LT ⁻¹
force = mass*acceleration = mass×(distance/time)/time= M*((L/T)/T) = MLT ⁻²

Mathematical Properties

Dimensional symbols, such as L, form a group: There is an identity, L⁰ = 1; there is an inverse to L, which is 1/L or L⁻¹, and L raised to any rational power p is a member of the group, having an inverse of L^−p or 1/L^p. The operation of the group is multiplication, with the usual rules for handling exponents (Lⁿ × L^m = L^n+m).

Indeed, dimensional symbols can be seen as a vector space over the rational numbers, with the coordinates of the vector being the powers of the exponents – expressing a dimensional symbol as MⁱL^jT^k corresponds to the vector (i,j,k). A basis for a given space of dimensional symbols is called a set of fundamental quantities or fundamental dimensions.