Chapter 1: Introduction to the Metric System

1.1 Introduction

Physics calculations often involve measurements of various physical quantities such as length, time, mass, and temperature. To make these calculations easier and more accurate, scientists have developed a system of units known as the metric system. This system has become widely used around the world and has many benefits over other systems of measurement.

1.2 How the Metric System Works

The metric system is based on a set of base units that are used to measure various physical quantities. These base units are:

• Meter (m) for length
• Second (s) for time
• Kilogram (kg) for mass
• Kelvin (K) for temperature
• Mole (mol) for amount of substance
• Candela (cd) for luminous intensity
• Ampere (A) for electric current

By using these base units, scientists can create a series of derived units that are used to measure other physical quantities. For example, velocity can be expressed as meters per second and force can be expressed as kilograms times meters per second squared

1.3 Benefits of the Metric System in Physics

The use of a consistent system of units like the metric system has several benefits in physics. Some of these benefits include:

• Consistency: By using the same units across different experiments and calculations, scientists can easily compare and combine results.
• Accuracy: The metric system is based on well-defined and standardized units, which reduces the potential for errors and inconsistencies in measurements.
• Simplicity: The metric system is easy to use and has a straightforward conversion system between different units. This makes it easier to perform calculations and convert between different units of measurement.

1.4 Prefixes of the Metric System

One of the key features of the metric system is its use of decimal-based prefixes. These prefixes denote multiples and submultiples of the base units, allowing for easy conversion between units of different magnitudes. This feature contributes to the simplicity and consistency of the metric system.

1.4.1 Expressing Larger Quantities

Below are some of the most commonly used prefixes in the metric system:

• Kilo- (k): Represents a factor of (or one-thousand). For example, 1 kilometer (km) is 1,000 meters (m).
• Mega- (M): Represents a factor of (or one-million). For example, 1 megameter (Mm) is 1,000,000 meters (m).
• Giga- (G): Represents a factor of (or one-billion). For example, 1 gigameter (Gm) is 1,000,000,000 meters (m).
• Tera- (T): Represents a factor of (or one-trillion). For example, 1 terameter (Tm) is 1,000,000,000 meters (m).
• Peta- (P): Represents a factor of (or one-quadrillion). For example, 1 petameter (Pm) is 1,000,000,000,000 meters (m).

The list keeps going, but these are the most useful prefixes to know when discussing really big numbers.

1.4.2 Expressing Smaller Quantities

On the other hand, the following prefixes are useful in discussing extremely small numbers:

• Milli- (m): Represents a factor of (or 0.001). For example, 1 millimeter (mm) is 0.001 meters (m).
• Micro- (): Represents a factor of (or 0.000001). For example, 1 micrometer (μm) is 0.000001 meters (m). Note: this prefix is the Greek letter “mu” and not the letter “u.”
• Nano- (n): Represents a factor of (or 0.000000001). For example, 1 nanometer (nm) is 0.000000001 meters (m).
• Pico- (p): Represents a factor of (or 0.000000000001). For example, 1 picometer (pm) is 0.000000000001 meters (m).
• Femto- (f): Represents a factor of (or 0.000000000000001). For example, 1 femtometer (fm) is 0.000000000000001 meters (m).

As you can see, it is much easier to write 1 fm rather than 0.000000000000001 meters. In fact, SI prefixes are even simpler than scientific notation. In other words, writing 1 fm is even easier than writing

The beauty of these prefixes is that they are consistent across all units of measurement in the metric system. For instance, the prefix “kilo-” means 1000 whether it’s used with meters (km) to denote length, grams (kg) for mass, or seconds (ks) for time. This consistency contributes to the ease of use and accuracy of the metric system, making it an invaluable tool in physics and other scientific disciplines.

1.4.3 Other Prefixes

You will notice that all of the prefixes above are in multiples of 3. This is an important tool of the metric system meant to simplify calculations. However, some other prefixes exist like the ones listed below:

• Hecto- (h): Represents a factor of (or 100). For example, 1 Hectometer (hm) is 100 meters (m).
• Deka- (da): Represents a factor of (or 10). For example, 1 Dekameter (dam) is 10 meters (m).
• Deci- (d): Represents a factor of (or 0.1). For example, 1 decimeter (dm) is 0.1 meters (m).
• Centi- (c): Represents a factor of (or 0.01). For example, 1 centimeter (cm) is 0.01 meters (m).

NOTE: Prefixes for quantities larger than one are capitalized. Prefixes for quantities smaller than one are lower case. So, a femtometer will always be written as 1 fm, never as 1 Fm. Similarly, one-billion Hertz would be expressed as 1 GHz, not 1 gHz. There are only a few exceptions to this rule. The prefixes kilo (k), hecto (h) and deka (da) use lower case.

1.5 Example Units in the Metric System

In physics, some of the more commonly used units include:

• Meter (m): Used to measure length, such as the height of a building or the distance between two points.
• Second (s): Used to measure time, such as the duration of a video or the time it takes for a ball to fall to the ground.
• Kilogram (kg): Used to measure mass, such as the weight of a person or the mass of an object.
• Newton (N): Used to measure force, such as the force exerted by a push or the force of gravity on an object.
• Joule (J): Used to measure energy, such as the energy needed to lift a weight or the energy released in an explosion.
• Watt (W): Used to measure power, such as the rate at which energy is being consumed or generated.
• Meter per second (m/s): Used to measure velocity, such as the speed of a moving car or the velocity of a projectile.
• Hertz (Hz): Used to measure frequency, such as the frequency of a sound wave or the frequency of light.
• Tesla (T): Used to measure magnetic field strength, such as the strength of the Earth’s magnetic field or the magnetic field generated by a magnetic material.
• Pascal (Pa): Used to measure pressure, such as the pressure of air in a tire or the pressure of a fluid in a pipe.

As you can see, some of these units come directly from the base units mentioned earlier. However, many derived units are similarly commonplace.

Chapter Summary

The metric system is an essential tool in physics and has many benefits that make it easier and more accurate to perform calculations. By using well-defined units, scientists can ensure consistency and accuracy in their experiments and calculations. Pay careful attention to prefixes and take the time necessary to understand them. This small investment will pay off immensely in the future.

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Homework 1 is available on Canvas here. It covers content from Chapters 1 through 4. It should be completed before moving on to Chapter 5.

Knowledge Check

Answer the quiz questions below.

Continue to Chapter 2: Introduction to Vectors

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