# 3 1.2 Physical Quantities and Units.

Mechanics is a quantitative science which means we will describe human movement and its causes using numbers. To provide information about a movement, we have to be able to specify how it is measured. For example, we define distance and time by specifying methods for measuring them, whereas we define average speed by stating that it is calculated as distance traveled divided by time of travel.

Measurements of physical quantities are expressed in terms of units, which are standardized values. For example, the length of a race, which is a physical quantity, can be expressed in units of meters (for sprinters) or kilometers (for distance runners). Without standardized units, it would be extremely difficult for scientists to express and compare measured values in a meaningful way. (See Figure 1 below.)

There are two major systems of units used in the world: SI units (also known as the metric system) and English units (also known as the customary or imperial system). English units were historically used in nations once ruled by the British Empire and are still widely used in the United States. Virtually every other country in the world now uses SI units as the standard; the metric system is also the standard system agreed upon by scientists and mathematicians. The acronym “SI” is derived from the French Système International.

# SI Units: Fundamental and Derived Units

The metric or SI system is administered in France by the Bureau International des Poids and Mesures or BIPM.   You can read more about them at  https://www.bipm.org/en/about-us/

Table 1 below shows the fundamental SI units that are used throughout this textbook.

Length Mass Time
meter (m) kilogram (kg) second (s)
Table 1. Fundamental SI Units.

It is an intriguing fact that some physical quantities are more fundamental than others and that the most fundamental physical quantities can be defined only in terms of the procedure used to measure them. The units in which they are measured are thus called fundamental units. In this textbook, the fundamental physical quantities are taken to be length, mass and time. All other physical quantities, such as force and velocity, can be expressed as algebraic combinations of length, mass and time; these units are called derived units.

# Units of Time, Length, and Mass: The Second, Meter, and Kilogram

## The Second

The SI unit for time, the second (abbreviated s), has a long history. For many years it was defined as 1/86,400 of a mean solar day. More recently, a new standard was adopted to gain greater accuracy and to define the second in terms of a non-varying, or constant, physical phenomenon (because the solar day is getting longer due to very gradual slowing of the Earth’s rotation).

## The Meter

The SI unit for length is the meter (abbreviated m); its definition has also changed over time to become more accurate and precise. In 1983, the meter was given its present definition (partly for greater accuracy) as the distance light travels in a vacuum in 1/299,792,458 of a second.  This change defines the speed of light to be exactly 299,792,458 meters per second. The length of the meter will change if the speed of light is someday measured with greater accuracy.

## The Kilogram

The SI unit for mass is the kilogram (abbreviated kg); it is defined to be the mass of a platinum-iridium cylinder kept with the old meter standard at the International Bureau of Weights and Measures near Paris.

In Biomechanics, all pertinent physical quantities can be expressed in terms of these fundamental units of length, mass, and time.

## Metric Prefixes

SI units are part of the metric system. The metric system is convenient for scientific and engineering calculations because the units are categorized by factors of 10. The table below gives metric prefixes and symbols used to denote various factors of 10.

Metric systems have the advantage that conversions of units involve only powers of 10. There are 100 centimeters in a meter, 1000 meters in a kilometer, and so on.

Prefix Symbol Value Example (some are approximate)
kilo k 103 kilometer km 103 m about 6/10 mile
hecto h 102 hectoliter hL 102 L 26 gallons
deka da 101 dekagram dag 101 g teaspoon of butter
100

(=1)

meter
deci d 10-1 deciliter dL 10-1 L less than half a soda
centi c 10-2 centimeter cm 10-2 m fingertip thickness
milli m 10-3 millimeter mm 10-3 m flea at its shoulders
Table 2. Select Metric Prefixes for Powers of 10 and their Symbols.

Physical quantities are a characteristic or property of an object that can be measured or calculated from other measurements.

• Units are standards for expressing and comparing the measurement of physical quantities. All units can be expressed as combinations of three fundamental units.
• The three fundamental units we will use in this text are the meter (for length), the kilogram (for mass) and the second (for time). These units are part of the metric system, which uses powers of 10 to relate quantities over the vast ranges encountered in nature.
• The three fundamental units are abbreviated as follows: meter, m; kilogram, kg; second, s. The metric system also uses a standard set of prefixes to denote each order of magnitude greater than or lesser than the fundamental unit itself.

# Glossary

physical quantity
a characteristic or property of an object that can be measure or calculated from other measurements
units
a standard used for expressing and comparing measurements
SI units
the international system of units that scientist in most countries have agreed to use; includes units such as meters, liters, and grams
English units
system of measurement used in the United States; includes units of measurement such as feet, gallons, and pounds
fundamental units
units that can only be expressed relative to the procedure used to measure them
derived units
units that can be calculated using algebraic combinations of the fundamental units
second
the SI unit for time, abbreviated (s)
meter
the SI unit for length, abbreviated (m)
kilogram
the SI unit for mass, abbreviated (kg)
metric system
a system in which values can be calculated in factors of 10 