Physics for Scientists & Engineers & Modern Physics, 9th Ed

Q 
uick Quiz 
1.2
True or False: Dimensional analysis can give you the numerical 
value of constants of proportionality that may appear in an algebraic expression.
Pitfall Prevention 1.2
Symbols for Quantities Some 
quantities have a small number 
of symbols that represent them. 
For example, the symbol for time 
is almost always t. Other quanti-
ties might have various symbols 
depending on the usage. Length 
may be described with symbols 
such as x, y, and z (for position); 
r (for radius); a, b, and c (for the 
legs of a right triangle); , (for the 
length of an object); d (for a dis-
tance); h (for a height); and
so forth.
Identify the dimensions of v from Table 1.5:
3v4 5
L
T
Example 1.1 
Analysis of an Equation
Show that the expression v 5 at, where v represents speed, a acceleration, and t an instant of time, is dimensionally correct.
S o L u t i o n

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1.4
conversion of Units 
9
1.4 
Conversion of Units
Sometimes it is necessary to convert units from one measurement system to another 
or convert within a system (for example, from kilometers to meters). Conversion 
factors between SI and U.S. customary units of length are as follows:
1 mile 5 1 609 m 5 1.609 km 
1 ft 5 0.304 8 m 5 30.48 cm
1 m 
5
39.37 in. 5 3.281 ft 
1 in. 5 0.025 4 m 5 2.54 cm (exactly)
A more complete list of conversion factors can be found in Appendix A.
Like dimensions, units can be treated as algebraic quantities that can can-
cel each other. For example, suppose we wish to convert 15.0 in. to centimeters. 
Because 1 in. is defined as exactly 2.54 cm, we find that
15.0 in. 5
115.0 in. 2 a
2.54 cm
1 in.
b 5 38.1 cm
where the ratio in parentheses is equal to 1. We express 1 as 2.54 cm/1 in. (rather 
than 1 in./2.54 cm) so that the unit “inch” in the denominator cancels with the unit 
in the original quantity. The remaining unit is the centimeter, our desired result.