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(M L 2 L 2 ) / (L 3 T 2 )
Canceling dimensions that appear in both the numerator and denominator yields:
M (L/T 2 )
which is consistent with the form shown earlier for resistance, R f . This exercise also
reveals that the empirical term, C f , for the coefficient of friction must be nondimensional
—that is, it is a constant number with no units.
With that, let's take a look at some more common physical quantities that you will be
using along with their corresponding symbols, component dimensions, and units in
both the SI and English systems. This information is summarized in Table 1-1 .
Table 1-1. Common physical quantities and units
Quantity Symbol Dimensions Units, SI Units, English
Acceleration, linear A L/T 2 m/s 2 ft/s 2
Acceleration, angular α radian/T 2 radian/s 2 radian/s 2
Density ρ M/L 3 kg/m 3 slug/ft 3
Force F M (L/T 2 ) newton, N pound, lbs
Kinematic viscosity ν L 2 /T m 2 /s ft 2 /s
Length L (or x, y, z) L meters, m feet, ft
Mass m M kilogram, kg slug
Moment (torque) M a M (L 2 /T 2 ) N-m ft-lbs
Mass Moment of Inertia I M L 2 kg-m 2 lbs-ft-s 2
Pressure P M/(L T 2 ) N/m 2 lbs/ft 2
Time T T seconds, s seconds, s
Velocity, linear V L/T m/s ft/s
Velocity, angular ω radian/T radian/s radian/s
Viscosity µ M/(L T) N s/m 2 lbs • s/ft 2
a In general, we will use a capital M to represent a moment (torque) acting on a body and a lowercase m to represent the mass of
a body. If we're referring to the basic dimension of mass in a general sense—that is, referring to the dimensional components of
derived units of measure—we'll use a capital M . Usually, the meanings of these symbols will be obvious based on the context in
which they are used; however, we will specify their meanings in cases where ambiguity may exist.
Coordinate System
Throughout this topic we will refer to a standard, right-handed Cartesian coordinate
system when specifying positions in 2D or 3D space. In two dimensions we will use the
coordinate system shown in Figure 1-1 (a), where rotations are measured positive coun‐
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