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Measurement
1. All physical quantities consists of a numerical magnitude and a unit.
2. Base Quantities
A base quantity is defined in terms of a standard. It is not defined in terms of other physical quantities.
The are seven base units defined in the SI system.
Mass-kg
Length – m
Time – s
Mole
Temperature – k
Luminous Intensity – cd
Current – A
3. Derived Quantities
A derived quantity in Physics can be obtained from the multiplication or division of the base quantities; no numerical factors are involved.
4. Homogeneity of physical equations
A physically correct equation must be homogenous.
A physical equation is said to be homogeneous if each of the terms separated by plus, minus or equality signs on the left and right side of the equation has the same dimensions, i.e., have the same base units.
i.e If the equation A = B + C is homogenous, than
the units of A = the units of B = the units of C
Note that you cannot add units together.
5. A physical equation may be homogeneous but it may be physically incorrect for the following reasons:
(a) it cannot find the value of dimensionless constants.
(b) combinations of quantities which end up dimensionless will not be revealed.
(c) only relationships which involves the product or quotient of physical quantities can be obtained. No information about exponential or logarithmic functions can be deduced.
(d) dimensional consistency does not, in general, validate a relationship.
From A level Physics Tutors
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