5
Force, weight, acceleration, velocity, and displacement are just few examples of vectors. Usually, a vector
is represented by an upper or lower case letter and an arrow on top. For instance, A, B or a , b . Figure
(1.3) shows a pictorial representation of a vector.
Figure 1.3: A vector v is represented by its length (magnitude) and direction. Credit: “Physics for scientists and engineers
strategic approach” by Randall D. Knight, Pearson-Addison Wesley 2004.
1.3 The Role of Measurements in Physics
Measurements in physical sciences are so important. It consists of comparing of a physical quantity like
length or mass with a standard or unit using a tool. The process of measurement consists of the following
four steps
1.
2.
3.
4.
Select a standard unit of measurement.
Follow a procedure or operation of how the comparison is made. Choose a tool of measurement
Count how many standard units that match the physical quantity.
Record the result. The result consists of numerical number and a unit.
The following example explains this procedure.
Example 1.1
Measure the length of your thumb
Solution
This example is concerned with the physical quantity length. Length can be measured by standard units of
centimeter, meter, kilometer, inch, foot, and mile. The choice must match the demand
1. Select the centimeter as the standard unit of measurement. This is a reasonable choice.
2. Follow a procedure or operation to measure (compare).
(a) Use a ruler or a measurement tape as a tool. Place the ruler parallel to and along your thumb so
that it lined up with the bottom edge of the thumb.
(b) Make a small pencil mark at the ruler at the point that matches the end of your thumb. You can
use your eye sight instead of the pencil mark.
3. Count how many centimeters are in the finger length. You come up with the number 3.2.
4. Record your final result: 3.2 cm
Caution: A number without unit carries no information and does not serve the purpose.