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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Richard Cardenas*

Richard Cardenas has taught Physics for 15 years. He has a Ph.D. in Physics with a focus on Biological Physics.

In this lesson, you will learn about what makes a number a scalar quantity. You will learn how to identify quantities that are scalars from those that are not scalar quantities. You will also learn about numbers that don't look like scalars but are actually scalars.

How tall is that building? How long did your trip take? How hot is it outside? All of these questions have one thing in common. All of the answers to these questions are called scalar quantities. A **scalar** is any quantity that only requires a magnitude or size to describe it completely. A scalar is any number that gives you the **size** or **magnitude** of a quantity, so a unit of measure must be attached to the number, like degrees or meters. Any random number is not a scalar. For example, the number 42 is meaningless unless you tell us that 42 is a measurement of something like distance or time or temperature.

You go to the grocery store to purchase half an avocado for your salad. You place the avocado on the scale and the scale reads 87.9 grams. The scale reads the mass of the avocado, and mass is an example of a scalar quantity. It gives you an idea about how much avocado you're purchasing.

Another example of a scalar is distance. Before driving to the grocery store, you zero out the trip meter of your car. When you return home from the grocery store, your trip meter reads 34.5 miles. The trip meter reads the distance traveled by your car. It gives you an idea of how far you traveled during your trip to the grocery store.

Average speed (or just speed) is another example of a scalar quantity. Speed is defined as the distance traveled divided by the time it took to travel that distance. It is a measure of a rate of change of your distance and has units of meters/second (m/s) or miles/hour (mph), or kilometers per hour (kph). Speed depends on distance and time, which are also both scalar quantities, therefore, speed is also a scalar quantity. For example, a long road trip covered a distance of 338 miles. You drove that distance in 5 hours. Therefore, your average speed for the trip was 338 miles divided by 5 hours, or 67.6 mph. These are all scalar quantities.

Scalar quantities do not specify direction like north or south, up or down, left or right. In physics, direction is sometimes indicated by a plus (+) or minus (-) sign in front of a quantity or an angle, such as 30 degrees. For example, -10 meters is not a scalar quantity because the negative sign indicates direction relative to some reference point. This reference point is also called the origin. The statement 10 meters to the left of the oak tree is an example of a non-scalar quantity because both a magnitude (10 meters) and direction (left) is specified in the statement, and the tree is the reference point or origin.

Time is an example of a quantity that does not seem to be a scalar but is actually a scalar quantity. Why? Because time is directional. Time flows in a specific direction. Temperature is another quantity that can be mistakenly called a non-scalar quantity. Why? Because we have positive and negative temperatures. However, the positive and negative signs of temperature do not indicate any direction. Instead, they indicate the relative magnitude of hotness or coldness. For example -30 degrees Celsius would make someone think of something cold while +100 degrees Celsius makes people think of something hot.

A number by itself, such as 25, is not a scalar quantity since it does not specify the magnitude or size of anything specific. In order for a number to be called a scalar, it has to have units specified. Kilogram, meters, and seconds are examples of units of mass, distance, and time. A number with a unit can then be called a scalar as long as it does not indicate any direction such as a plus or minus sign, or a north, south, east, or west for example.

To summarize, any quantity that can be completely described by its **magnitude** only is considered a **scalar quantity**. This can include things like distance, time, speed, and temperature. If additional information is needed to adequately describe the quantity, it can no longer be called a scalar quantity. Directions like up, down, left, right, north, or south would be examples of non-scalar quantities.

Terms | Definitions |
---|---|

Scalar | any quantity that only requires a magnitude or size to describe it completely |

Size / Magnitude | a unit of measure must be attached to a number to make it scalar |

Scalar quantity | any quantity that can be completely described by its magnitude |

Non-scalar quantity | a quantity that needs additional information to describe the quantity; things like distance, time, speed, or temperature are examples |

Fortified with knowledge of this lesson, take the opportunity to ensure that you can:

- Describe a scalar
- Provide examples of scalars
- Contrast scalar and non-scalar quantities
- Point out the fact that lone numbers are not scalars

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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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