Note 1 to entry: A power of a factor is the factor raised to an exponent. Each factor is the dimension of a base quantity.
Note 2 to entry: The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in roman (upright) sans-serif type. The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a quantity Q is denoted by dim Q.
Note 3 to entry: In deriving the dimension of a quantity, no account is taken of its scalar, vector or tensor character.
Note 4 to entry: In a given system of quantities,
Note 5 to entry: In the International System of Quantities (ISQ), the symbols representing the dimensions of the base quantities are:
Base quantity
Symbol for dimension
length
L
mass
M
time
T
electric current
I
thermodynamic temperature
Θ
amount of substance
N
luminous intensity
J
Thus, the dimension of a quantity Q is denoted by dim Q = LαMβTγIδΘεNζJη, where the exponents, named dimensional exponents, are positive, negative, or zero. Factors with exponent 0 are usually omitted. When all exponents are zero, the symbol 1, printed in sans-serif type, is used to represent the dimension. Examples are:
Note 6 to entry: An exponent can be fractional.
The period T of a pendulum of length l at a place with the local acceleration of free fall g is:
T=2π√1g or T=C(g)√l where C(g)=2π√g
Hence dim C(g) = T· L−1/2.
T=2π 1 g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmGadiWaaiWabaabaiaafaaake aacaWGubGaeyypa0JaaGOmaGWaaiab=b8aWnaakaaabaWaaSaaaeaa caaIXaaabaGaam4zaaaaaSqabaaaaa@3FBD@ or T=C(g) l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmGadiWaaiWabaabaiaafaaake aacaWGubGaeyypa0Jaam4qaiaacIcacaWGNbGaaiykamaakaaabaGa amiBaaWcbeaaaaa@3F85@ where C(g)= 2π g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmGadiWaaiWabaabaiaafaaake aacaWGdbGaaiikaiaadEgacaGGPaGaeyypa0ZaaSaaaeaacaaIYaac daGae8hWdahabaWaaOaaaeaacaWGNbaaleqaaaaaaaa@4136@