Chapter 1: Introduction Reference Tools & Resources

Reference Tools & Resources

I. Key Terms and Phrases

physics: the study of the fundamental laws of nature and many of their applications.

SI units: the internationally adopted standard system of units (based on meters, kilograms, and seconds) for quantitatively measuring quantities.

dimension of a quantity: the fundamental type of a quantity such as length, mass, or time.

dimensional analysis: a type of calculation that checks the dimensional consistency of an equation.

significant figures: the digits in the numerical value of a quantity that are known with certainty.

scientific notation: a method of writing numbers that consists of a number of order unity times the appropriate power of ten.

conversion factor: a factor (equal to 1) that multiplies a quantity to convert its value to another unit.

order-of-magnitude: the power of ten characterizing the size of a quantity.

II. Miscellaneous Tips

(A) Dimensional Analysis

You should be aware that typically, arguments of mathematical functions are dimensionless. Angles, for example, are dimensionless as can be seen by the equation for the length of a circular arc s = rq, where q is in radians. Hence, angular measures like radians and degrees only signify how we choose to measure the angle. The trigonometric functions, therefore, such as sine, cosine, and tangent are applied to dimensionless quantities. Other examples of dimensionless functions are log(x), ln(x), and their inverse functions 10^x and exp(x).

(B) Round-off Error

Above it was stated that excessive round-off error can often be avoided by keeping at least one additional figure in intermediate calculations. An often better approach to this is to avoid calculating numerical values in intermediate steps. Instead, just carry through the formulas from the intermediate steps and only plug in numerical values once at the end. You will see examples of both approaches throughout this study guide.

Example 1.7 Don't Round-off too Soon: A cardboard box has a base that measures w = 1.92 m, and d = 0.725 m. If its height is h = 1.88 m. (a) Calculate the area of the base of the box. (b) Calculate its volume using the result of (a). (c) Calculate its volume using the formula for volume.

Picture the Problem The diagram shows a box representing the box whose base area and volume we wish to determine.

Strategy We shall first calculate the area of the base.

Solution

(a) Calculate the area of the base:	area = wd = 1.92 m x 0.725 m = 1.39 m2
(b) The volume of the box is area x height:	vol = area x h = 1.39 m2 x 1.88 m = 2.61 m3
(c) The volume is length x width x height:	vol = area x h = wdh = 1.92 m x 0.725 m x 1.88 m = 2.62 m3

Insight The answers to parts (b) and (c) differ in the final digit. Which one is correct? Part (c) is correct because the full values were used. The round-off to three significant figures in part (a) is the reason for the difference.

Reference Tools and Resources by David Reid, Eastern Michigan University. ©2002 by Prentice Hall, Inc.

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