Measuring Things
From Perspectives in Physics and Physics Education
One of the most important aspect of physics is making measurements of physical quantities. What are measurements? How should we talk about them? What can we measure? Why should you measure anything? Is it even practical or useful to measure anything?
Measurements are the cornerstone of science since science is the study of the natural world. We must measure things in order to be able to speak about them constructively and meaningfully.
The following is the first article in the Perspectives in Physics and Physics Education series, and is quintessentially an introduction to science.
Everyday versus Scientific Conversation
We talk imprecisely about measurements in everyday conversation but rarely think about such quantities in specific scientific terms.
Here are some examples:
“The weather is nice today” (Temperature?)
“It takes forever to get home after work.” (Time?)
“These shoes are too small for my feet.” (Length? Width? Height?)
“I’d like a piece of cake.” (What size?)
“I love the feel of cool sheets on my bed at night.” (Temperature?)
“I ran down the hill so fast I tripped.” (Speed?)
In science, we’re interested in knowing exactly what you mean. Words referring to measurements have specific meaning. They’re part of our scientific conversation and have different meaning in everyday conversation.
For example, in everyday conversation you might use the word pressure to indicate social influence on a runner, such as “He was under pressure to win the race.”
A physicist might more quantitatively describe the actual event and say, “He was under one atmosphere of pressure during the race.”
While the physicist’s statement is often considered a bit absurd in an everyday conversation, it is an accurate description of the event that describes the pressure under which the runner was subjected during the event. The pressure is a specific physical, measurable quantity.
Thus, an important aspect of science is to begin thinking about the meaning of words in a scientific sense and not assume they mean the same in everyday conversation.
In science, it’s important to be very specific about what you mean when describing physical quantities and properties of things. For this reason, as a physicist, I try to take great care in not only selecting appropriate words to describe things, but I also think intimately about words themselves and how words are entities all their own. Some of my thinking in these terms is found in Poetry in the Wild.
What is a Measurement?
When you think about measurements, what comes to mind?
A tape measure to measure the length of a board when building a house?
A measuring cup in your kitchen to measure the amount of water you need to add to a cake batter?
In science, a measurement is the act of assigning a number to something. A number is a piece of information you could give someone else. You don’t need to give them the thing you measured — just the number.
The key to this exchange of information, however, is that you must both agree on what the number means.
For example, let’s suppose your friend wants to know about your pet donkey. After you do a measurement of your donkey, you tell her “four hundred fifty-two.” What does that mean to your friend? Did you weigh the donkey? Did you measure its length? Did you take its temperature? Maybe you told her its age?
Thus, you need to both know what you measured.
Here are some things we can measure:
Height of a building
Length of a bridge
Time elapsed during a jump
Speed of a running dog
Pressure of air on your hand
Weight of an American nickel
Distance between Chicago and Seattle
Mass of the planet Venus
Time between sunrise and sunset
Temperature of water in a pan.
So the next time you tell someone about a measurement you made, be sure you also let them know precisely what you measured.
Why Do We Measure Things?
The simple answer of why we measure things is to make things easier.
Seriously. Here’s an example. Suppose you want to move a desk from your kitchen to your bedroom. Will the desk fit between your bed and the wall of your closet? If you look at the picture below, you’ll realize it could be a pretty tight spot, and you don’t want your bedroom door to bang into the desk every time you open it.
You could just move the desk across your apartment or house, maybe up a flight of stairs, and see if it’ll fit. That sounds like a bit of unnecessary work when you’re not sure of anything at all.
You could also just look at it and believe it’ll fit in your bedroom where you want it. This is sometimes called “eye-balling it.” Eye-balling it may work about half the time, but if you’d like to be right 100% of the time, you’ll want to do some quick measurements.
If you’re really good, you might also check the widths of doorways to be sure the desk will even pass through them. Trust me. As a guy who moved and helped others move dozens of times from one dorm room to another, one apartment to another, and one house to another, it’s best to do some measurements to be sure your things will even get through doorways and plan to orient big furniture and appliances in just the right way before you get them to the doorway, stairway, or back alley.
The worst case I had was moving a washer and dryer off my rental van by myself, down a narrow flight of stairs into a tighter space with a cinder block wall just feet from the foot of the stairs, then to the left through an even narrower doorway. I had to use two moving dollies and ensure I was in the right place at the right time while moving it by myself as there was no room to climb over it on the way down the stairs nor through. I measured everything and got it done like a pro, starting with the lighter dryer. Then I repeated the process with the heavier washer.
So, what measurement can you do before moving your desk? You might not have a measuring tape because you’re new to all this “measurement stuff,” so just grab a long string or anything long and narrow you can take with you to your bedroom from the kitchen.
Compare the length of the string to the length of your desk. Mark the length. Take the string to your bedroom and see if it will fit nicely between the closet wall and your fully open bedroom door. If the door can’t be opened fully, is it good enough, or do you want to avoid the problem of a door banging against your desk altogether?
We Also Measure to Compare Things
We also measure things so we can compare one thing with another.
For example, suppose your friend wants to know if the desk in their dining room is longer than the desk in your kitchen. You can measure the length of your desk with a piece of string and cut to that length. You can then give your friend the string and ask them to compare it to the length of their desk.
Once your friend compares your length of string to the length of their desk, they report back to you that their desk is shorter in length, but a little more than half the length of the string.
That information isn’t too bad. If your friend was donating their desk and was considering your offer to sell or give them your desk, they could use the string to determine if your desk will fit in their dining room, or vice versa. You might want a shorter desk, and now you know theirs is shorter, so you could put it where your kitchen desk is once you remove your desk.
But how can we get the most use of this idea of making measurements?
If your friend lived in another country or state, you’d have to send your string to them so they can compare it to the length of their desk. That’s possible, but it could become a very long process. Every time you wanted to compare lengths of things with your friend, you’d have to cut a new string and send it to them.
That’s not a very practical nor useful way to compare measurements.
You need a way to make your strings more accessible to your friend.
Make Measurements Useful and Practical
If your process of string-cutting and sending lengths of string to your friend is ever to be a useful and practical way to exchange information about the lengths of things with your friend, you might decide that the first string you send to them is a standard length.
Then, if your friend cuts the standard length in half, that’s half the standard length. Cutting each of those halves in half will be quarter-lengths of your standard length, and so on.
Eventually, you and your friend agree that the standard length is not only useful and practical, but it’s also accessible to both of you.
This standard of length becomes a unit of length. Perhaps you’ll call it a meter.
In fact, we’re free to define a standard unit any way we want. We used a string that happened to be the same as the length of your kitchen table. But is it a useful and practical unit of length?
Is it useful to do something without actually moving the thing (like your desk)?
It is useful for measuring small things like the size of atoms if you cut into smaller and smaller equal-sized bits?
Could you measure the distance to Mars with it?
Does the length of the string ever change?
We need a standard unit of measurement that meets all these criteria.
Ultimately, we’ll want a standard unit of measurement for every kind of measurement we can make. Temperature. Time. Weight. Mass. Speed. . . .
Some Unusual (But Useful!) Units of Measurement
shake (very short period of time) Comes from the expression “two shakes of a lamb’s tail.” In nuclear engineering, 1 shake = 10 nanoseconds.
mil (length, often a thickness) More commonly a mil is called a thou and is a thousandth of an inch (0.001 inch). The term “mil” is used more commonly in the U.S. and is confused with millimeter by novices. You may have noticed the thickness of sheets of plastic or the thickness of plastic bags are often labeled in units of mils.
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nines (number of 9s in a number less than one) For example, the purity of a material sample might be “3 nines” which means 0.999, or 99.9%, pure. This is commonly used in the semiconductor and scientific gases industry.
foe (amount of energy) Typically used in astrophysics to measure the amount of energy released when a star explodes (a nova). A supernova may release about one foe of energy per second.
Standard Units of Measure
The procedure we devised for creating a way to measure things using a standard string length wasn’t a bad start.
One issue we have is that in order to measure things, we’d have to cut the standard string into progressively smaller halves. That’s pretty destructive.
Another issue is that when our string gets wet, it’s length changes. And once we dry it out again, its length isn’t quite the same as before.
In order for our standard unit of measure to be useful and practical, we need to create specific procedures to be sure any measurement can be expressed in terms of this standard.
What if we create a length of a rod of material that’s the same length as our standard string length? We will want to choose a material that doesn’t expand too much when it gets hot or contract too much when it gets cold.
If different people used such a rod at different places around the world, they’d report measurements we couldn’t reliably compare to measurements from others. What if we tell everyone that the standard rod length is measured at a particular temperature? Then everyone could make sure their rod is at that particular temperature.
Other questions about the rod length are important to consider. Does atmospheric pressure affect the length of the rod? Does the time of day, position of the moon, or humidity of the air surrounding the rod affect its length?
All these things are considered when we create a standard unit of measure.
So Many Things to Measure — and No Time (yet)
There are so many things to measure. To organize them, we define all measured quantities in terms of a small number of other quantities.
Consider what quantities we would need to create a standard unit of speed. We might try creating a standard unit of speed by measuring the speed of a running dog. What quantities do we need to do this?
First, we need a dog. A dog isn’t a quantity, but it is the thing on which we’ll base our measurements.
Second, we’ll have the dog run over a certain distance. We could use our standard unit of length to do this. So we’ve got a good start. Maybe 100 meters?
Third, we’d need to measure the time it takes the dog to run across 100 meters. So we’ll need to devise a standard unit of time. How would you do that? Be sure your standard time unit is accessible to as many people as possible, and make sure everyone can reliably compare it with everyone else’s measured times — they must not vary.
Ultimately, we’d use your standard unit of time and the meter rod to define a standard unit of speed. But since we can define speed in terms of length and time, we don’t actually need a standard unit of speed.
The standard units of length and time are called base standards because units of speed can be defined in terms of them.
In science, we define base standards.
Base Standards
Base standards of measurement must not vary and must be accessible to everyone.
There are only 7 base standards needed to represent all measurable quantities in science! These are:
- Length
- Time
- Mass
- Electric Current
- Temperature
- Amount of Substance
- Luminous Intensity
These will be discussed in another article.
Become a Pro
After all this thinking and discussing, we’ve come to realize something.
When we measure something, there are two important things to include when we report our measurement:
Unit of measure and the number of units.
Conventionally we write measurements in the order of number then units because it answers the question “how many units?” So, “10 units of centimeters” is written “10 centimeters.” Here are some examples.
- Height of building: 1234 centimeters
- Length of a bridge: 20 meters
- Time elapsed during a jump: 245,453 microseconds
- Speed of a running dog: 36 miles/hour
- Pressure of air on my hand: 1 atmosphere
- Weight of an American nickel: 5.0 grams
- Distance between Chicago and Seattle: 2770 kilometers
- Mass of the planet Venus: 4867000000000000000000000 kilograms
- Time between sunrise and sunset: 12.67 hours
- Temperature of water in a pan: 80 °F
While these are all correct ways to write measurements, some of them aren’t very useful nor practical. Can you guess which ones are not very practical ways to write measurements? I’ll discuss this in another article.
A Few Closing Remarks
Abbreviations or Symbols
There are many abbreviations for the units written above. Only one of them is written with its correct abbreviation, or symbol: °F, or “degrees Fahrenheit”
Writing the others with their correct unit symbols follows:
- Height of building: 1234 cm
- Length of a bridge: 20 m
- Time elapsed during a jump: 245,453 μm
- Speed of a running dog: 36 mi/hr
- Pressure of air on my hand: 1 atm
- Weight of an American nickel: 5.0 g
- Distance between Chicago and Seattle: 2770 km
- Mass of the planet Venus: 4867000000000000000000000 kg
- Time between sunrise and sunset: 12.67 hr
Space: The Final Comment
When writing a measurement, it is standard and grammatically correct to always separate the numerical value from the unit of measure with a space. For example, while it’s become common to see no space between the numerical value of the air temperature and the units in your favorite weather app, like 76°F, it’s standard and grammatically correct to write it like this: 76 °F.
A space between the value and unit symbol is required by the governing system of units, called the International System of Units (SI). Include the space to at least look like a pro.
