### Video Transcript

In this video, we’ll be talking about tools that are used to make measurements. Some of them will be more familiar than others, but they all have in common that they’re used to measure physical quantities. There are all source of such quantities, but we’re going to focus on three: length, time, and mass. The tools we’ll be looking at are designed to make these kinds of measurements. And for each of these three categories, we can think of some tools that measure that quantity, either length or time or mass.

For example, we likely have experience using a ruler to measure lengths. And along with this, we’re going to learn about a device called a Vernier caliper, as well as a device called a micrometer, which also are used to measure lengths. When it comes to measuring time, we saw on our opening screen a device used for doing that called an hourglass timer. Other ways to do this include using a pendulum clock, sometimes called a grandfather clock and also a digital stopwatch.

When we think about measuring masses, the tools used for doing this may be less familiar than those we use for measuring lengths and times. But they’re nonetheless quite useful. Two of those tools we’ll learn about in this lesson are the spring scale and the beam balance. It’s important to note that these lists aren’t exhaustive for the different tools we have for measuring these quantities. But since these are some of the more common tools, we’ll focus on these.

Let’s begin by considering the tools we use to measure lengths. We mentioned that rulers are one of the more common tools for measuring this quantity. Whenever we use a ruler to measure a length, it’s important to look at the scale the ruler is marked in. The scale is what tells us how far apart the numbered markings on the ruler are.

For a ruler marked out this way, if we wanted to measure the maximum length of some object, then we would start out by lining up the edge of that object with the zero marking on the ruler. And then rotating the object or the ruler so that the object’s maximum length is along a line parallel to the edge of the ruler. Lined up this way, we would find where the tip of our object to the right lines up with our ruler edge and record that value to the smallest distance scale marked out on our ruler. In this case, that’s centimeters. So, we would record this object’s maximum length as nine centimeters.

But then, oftentimes, a ruler is marked out with greater precision. It’s not uncommon to find rulers marked out in centimeters but with smaller marks in between each centimeter marking. Here, we have a close-up view of what those markings might look like between eight and nine centimeters. If we start out at the eight-centimeter mark and count the smaller marks, then we count one, two, three, four, five, six, seven, eight, nine of these marks before we get to the next whole centimeter marking. In other words, the smaller marks divide up one centimeter into 10 even chunks.

That means each one indicates a tenth of a centimeter or one millimeter of distance. If marks like these are in place, they let us record the length of our object with greater precision. Instead of reporting that length to the nearest centimeter, which is what we were doing before, now we can record that length to the nearest tenth of a centimeter. We see that our pink measurement line lines up most closely to this small mark here. And since that’s nine-tenths of the way between eight and nine centimeters, with these extra markings, we would record our object’s length as 8.9 centimeters.

Now, in order to show the differences between these various tools for measuring lengths, next to each tool, we’re going to write in a standard measurement resolution that they allow. These resolutions that we’ll write in aren’t guaranteed if we use one of these tools. For example, we’ve already seen with rulers that some have resolutions to the nearest centimeter, while others with more finely graded markings like these can measure to the nearest millimeter.

So, the resolution we’ll write in for each tool will be a standard but not a certain value. All that said, many rulers are marked out to the nearest millimeter. And therefore, they let us measure lengths to that resolution. So, that’s how rulers let us measure length. Now, what about this tool called a Vernier caliper?

Just to get a sense for these tools, this is what a standard Vernier Caliper looks like. It offers several different ways of measuring lengths, but perhaps the most common one is to insert the object whose length or other dimension we want to measure in between these two pieces here called jaws. And then, close the caliper jaws on that object so that its length, in this case, this dimension, can be measured.

Now, if we look closely at this caliper, we can see that it measures lengths in two different units. The top edge of the caliper is marked out in units of inches, while the bottom edge is marked out in centimeters. Now, this part of the caliper here that we have these arrows pointing to is called the main scale of the caliper. And really, the main scale is not very much different from a ruler.

But then, along with that main scale, there’s this bit here. A close-up view of this part shows us a second measurement scale, which, as we’ll see in a moment, lets us measure object lengths more precisely than we could if we just use the main scale. This second scale is called the Vernier scale. And on this particular pair of Vernier calipers, we’re told that this Vernier scale divides up into 20 equal parts the smallest difference in markings on our main scale.

And on that main scale, we saw that while these main numbered markings are one centimeter apart, we can see that each of these centimeters is divided up into 10 equal parts by smaller hashes. This means that the best resolution of our main scale, as we found with our ruler, is one millimeter, one-tenth of a centimeter. And this marking on our Vernier scale here tells us that by making a measurement using this scale, we’ll be able to record lengths to the nearest one twentieth of one millimeter. In other words, our best resolution with this instrument will be 0.05 millimeters.

To see how all this works, let’s go through the process of making an example measurement using these calipers. Let’s say that we have a wooden peg. Say that this is our peg and we want to measure its length. That is, we want to know this dimension. In that case, we would put one end of our peg against this jaw of our caliper and then close the other jaw shut on the peg so that now it’s firmly fixed between these two jaws.

At this point, we need to be careful to avoid a common measurement error using Vernier calipers. We might think that since one end of our object is here, then to measure the object’s length we find where the other end of the object meets the main scale. But if we record this value as the length of our peg, then we’ll have made a mistake. And that’s because this first end of our object here doesn’t actually line up with the zero marking on our main scale.

So, to correctly record this object’s length, what we do is we look at the zero marking of our Vernier scale here, and we see where that line crosses our main scale markings. Wherever it does, we record that main scale marking that is immediately to the left of the zero on our Vernier scale. In this case, that would be this main scale marking right there. And based on the way our main scale is divided up, that’s 2.5 centimeters.

So, the overall length of our peg, we can call that length 𝐿, is equal to 2.5 centimeters plus some value that we’re about to figure out. This additional value will come by making a reading on our Vernier scale using its increased resolution. So, we could say that this part of the length of our object comes from our main scale reading. And then, we could say that this part comes from the Vernier scale.

So, how do we read this scale here? The way we do it is by comparing the positions of the markings on our main scale with those on our Vernier scale. We look to see where those markings line up. What we do then is we visually scan across our Vernier scale. And we look to see where the markings on that scale line up with those on the main scale.

For example, look at the Vernier scale marking of one. We see that that doesn’t quite line up with the markings on our main scale, neither does the marking of two. That’s slightly offset. The marking of three is closer. But we see, as we go farther on, that actually we can do better. Look at the marking of four on our Vernier scale and how well it lines up with a mark on our main scale. If we go on to the mark indicated by five, we see that this doesn’t line up with the mark on the main scale quite so well. Neither does the one on six or seven or eight or nine and so on. The very best lining up, the very best agreement then, between our two scales is here at the four mark on our Vernier scale.

Now, if we were to look even more closely at this portion of our scale, we can see these marks lining up a little bit more clearly. This tells us that the length we want to add here — which, when added to this length, will give us our overall length — is indicated by the four marking position on our Vernier scale. We can now recall that each one of these individual adjacent markings on our Vernier scale corresponds to one twentieth of the smallest measurement difference on our main scale. That measurement difference was one millimeter. And so, each one of the etched markings on our Vernier scale corresponds to one twentieth of that.

Now, here’s another place where we’ll need to be careful. This marking of four actually doesn’t correspond to the fourth marking on our Vernier scale. That’s because each whole number on this scale, three and four and five and so on, actually has a marking between it and the next whole number over. And it’s the distances between these smallest marking differences that correspond to one twentieth of a millimeter.

This means, if we go back to our only slightly zoomed in view of our Vernier scale, that the mark indicated by four here, if we start at zero, is one, two, three, four, five, six, seven, eight marks up the scale. So, that means we take our smallest difference in distances indicated by our scale, and we multiply it by eight. One twentieth of a millimeter is 0.05 millimeters. And multiplied by eight, that’s 0.40 millimeters. So, it’s this value that we add to our main scale reading in order to get the overall length of our peg.

Now, 2.5 centimeters is the same thing as 25 millimeters. So, using these Vernier calipers, our final measured length of this peg would be 25.40 millimeters. And the maximum resolution of this tool, as we saw, was one twentieth of a millimeter.

So, we’ll write that as a standard-length resolution possible using a Vernier caliper. So, we’ve seen that a Vernier caliper uses an additional scale called the Vernier scale to add precision to its measurements. Now, we’ll look a device called a micrometer, which works in a similar way.

To measure a length using a micrometer, we take our object of interest, and then we close our micrometer in on it, just like we did with the lower jaw of our caliper. Once this is done, we read off a value indicated on the main scale of our micrometer. If we take an up-close view of this scale, the reading we record is of the last vertical mark on that scale, in this case, this mark here.

For micrometers, it’s typical for the distance between this mark and the similar one adjacent to it to be one millimeter. And then, for the distance between this mark and the one on the other side of this line from it to be half that, one-half of a millimeter. So, the main scale reading on a micrometer gives us a value that is correct to within one-half of one millimeter.

It’s at this point that the reading on the other scale, called the thimble scale, comes in. The reason for this name is that this scale can be rotated to adjust the position of our micrometer when we’re making a measurement. The markings on the thimble scale indicate smaller length differences than those on the main scale. In particular, they divide up this smallest length difference on the main scale — which, as we said, is often half of a millimeter — into some number of equal parts.

Often, on the thimble scale, there are 50 markings. If we go all the way around the thimble, which means that each marking indicates one fiftieth of one-half of a millimeter. Now, instead of 50, there might only be, say, 25. In that case, the markings divide up into 25 even parts, this smallest difference on the main scale. In this way, the thimble scale on a micrometer works like the Vernier scale on a Vernier caliper. And also like that caliper, when we make a reading with the micrometer, we record our main scale value and then add to it the value indicated on the finer scale.

When our thimble scale does have 50 evenly spaced markings on it, this means the maximum resolution our instrument can achieve is one one hundredth of a millimeter. This is equal to 10 microns, 10 millionths of a meter. So, if we record one one hundredth of a millimeter as a standard achievable resolution using a micrometer. Then we can see that the measurement resolution of these tools increases as we go from ruler to Vernier caliper to micrometer. Now that we’ve looked at different tools for measuring lengths, let’s look at a few for measuring times.

We can recall that these tools included an hourglass timer, a pendulum clock, and a digital stopwatch. Each of these tools measures time at different levels of precision. For example, hourglass timers are generally expected to keep time to the nearest minute. So, we might purchase a three-minute timer or a five minute or a 15 minute. We can say then that keeping time to the nearest minute is what hourglass timers are capable of.

A pendulum clock, though, which uses a pendulum that swings back and forth to keep time, is typically equipped with both an hour, a minute, and a second hand. It’s fairly standard for an entire period of the pendulum, that is, the time it takes for the pendulum to swing all the way in one direction and then all the way back, to be two seconds. The consistency of this period over time allows a pendulum clock to accurately measure times to the nearest second.

And then, even more precise than this is a digital stopwatch. Stopwatches are commonly equipped to be able to measure to the nearest one hundredth of a second. So, depending on the precision we would need in measuring time, we could either use an hourglass timer, a pendulum clock, a digital stopwatch, or even some other time measuring device.

Finally, let’s look at some different tools for measuring masses. Tools for measuring the mass of an object include a spring scale and also a beam balance.

Inside a spring scale, there is a spring, which is set up so that certain spring extensions are calibrated to certain mass values. So, if we hang some mass on the hook at the end of our spring scale, then in order to support the weight of that mass, the spring is extended. And that extension amount corresponds to a measured mass value.

Now, in terms of the resolution of a spring scale, the scale we’re looking at here measures to the nearest kilogram. But depending on the spring inside the scale, this can vary. A spring scale may be marked out in kilograms or grams. And there’s no one measurement resolution that we could say is standard.

The situation is similar with our other mass-measuring device, the beam balance. When we put an object with some amount of mass on our beam balance. We measure that mass by adjusting the position of a series of counterweights which, when they’re positioned properly, will let the arm of our balance line up with a fixed mark. Depending on the number and size of balancing arms, a beam balance could measure very small or very large masses. Once again then, we would say that measurement resolution varies.

Let’s summarize now the measurement tools we’ve looked at. In this lesson, we looked at tools for measuring length, time, and mass. We saw that three ways to measure length are to use either a ruler, a Vernier caliper, or a micrometer. And we also identified standard measurement resolutions of these tools.

We did the same thing for devices used to measure time. We saw that hourglasses can measure time to the nearest minute. Pendulum clocks do it to the nearest second. And then, of these time-measuring tools, stopwatches are the most precise, capable of measuring times to the nearest one one hundredth of a second. And lastly, we looked at tools for measuring mass. We saw that both of these tools, the spring scale and the beam balance, are able to measure masses with varying levels of precision.