In this explainer, we will learn how to identify different tools for the measurement of fundamental physical quantities.
Fundamental physical quantities (also called base quantities) are those that cannot be obtained by combinations of other fundamental quantities.
The following is a list of the SI base quantities:
- Amount of substance
- Absolute temperature
- Electric current
- Luminous intensity
In this explainer, we will only be considering length, time, and mass.
The explainer is specifically concerned with how length, time, and mass can be measured using different tools and devices.
Length is measured using an instrument that is graduated with markings that correspond to submultiples of a unit of length, the SI base unit of which is the metre.
A ruler is a straight-edged stick with graduated marks. An object for which the length is to be measured is placed along the straight edge and the number of marks between the ends of the object are counted.
The marks on a ruler are usually 1 millimetre (1 mm) apart. Usually, every 5 mm, the mark is larger to make it easier for a user to keep track of how many marks have been counted. Also, an even larger mark is usually made every 10 mm; these even larger marks are 1 centimetre (1 cm) apart. The following figure shows an enlarged section of a ruler on which the marks can be seen.
The maximum length that can be measured by a ruler in a single measurement is the length of the ruler. The minimum length that can be measured by a ruler is the smallest graduation of the marks on the ruler, usually 1 mm.
To measure lengths of less than 1 mm, different measuring devices are required. One such device is a vernier caliper, which is shown in the following figure.
The length measured by a vernier caliper is the distance between the jaws of the caliper. One jaw of the caliper, called the sliding jaw, can be moved away from and toward the fixed jaw so that the distance between the jaws equals the length of an object. The following figure shows the jaws of the caliper with an object between them.
The red arrow between the jaws of the caliper is equal to the length of the object between the jaws. A green arrow of the same length as the red arrow is shown on a graduated length of the caliper that is called the main scale.
The main scale of the caliper is the same as the scale of a ruler. The marks are 1 mm apart and every 10 marks a centimetre mark shows the length in centimetres.
Close inspection of the main scale of the caliper shown reveals that the length is somewhere between 34 mm and 35 mm. The main scale cannot measure a shorter length than this. There is, however, another scale on the caliper that moves with the sliding jaw. This scale is called the vernier scale.
The following figure shows where the main scale and the vernier scale meet. The vernier scale is outlined in a dashed orange box.
The vernier scale consists of 10 marks. Each mark on the vernier scale is some horizontal distance from the nearest mark to it on the main scale. One mark on the vernier scale has a smaller value for this distance than any of the other marks. This mark is the best aligned mark.
The best aligned mark corresponds to a value between 0 and 9 on the vernier scale. This value corresponds to a length expressed in tenths of a millimetre; if the best aligned mark is the mark labeled 3 on the vernier scale, the vernier scale reads a length of mm. The vernier scale shown here can therefore measure lengths as small as one tenth of a millimetre.
Let us now look at an example in which a vernier caliper is used to measure a length.
Example 1: Measuring a Length Using a Vernier Caliper
What is the length of the object being measured by the vernier caliper in the diagram?
To obtain the reading on the vernier caliper, we need to record the reading on the main scale and on the vernier scale.
In the following figure, the main scale reading is shown within a dashed red box.
We can see from the main scale that there are more than 27 marks between the start and the end of the reading, but less than 28 marks. The reading is closer to 28 marks than to 27 marks. The reading on the main scale is 27 mm, or 2.7 cm.
In the following figure, the entire vernier scale is shown within a dashed blue box.
The vernier scale consists of the graduated marks that range from 0 to 10. The reading on this scale corresponds to the mark for which there is the least horizontal distance between it and the closest mark to it on the main scale. The appropriate mark is indicated in the following figure.
This mark is the 9th on the vernier scale. Marks on the vernier scale correspond to lengths of a tenth of a millimetre, so this reading is 0.9 mm, or 0.09 cm.
The full reading on the caliper, in centimetres, is given by
Another length-measuring device that can measure distances of less than 1 mm is an instrument called a micrometer.
Perhaps unhelpfully, the name of this instrument is the same as the name for one-millionth of a metre, as “micro” means “one-millionth.” Less helpfully still, the instrument called a micrometer cannot measure lengths as small as one-millionth of a metre!
The following figure shows a micrometer and the names of its most relevant parts when using it to measure a length.
The object that the length of is to be measured is placed between the anvil and the spindle. The thimble is then turned until the gap between the anvil and spindle equals the length of the object.
When the thimble is turned, it moves along the sleeve. The main scale of the micrometer is on the sleeve. The rotating scale of the micrometer is on the thimble. As with vernier calipers, one mark on the rotating scale will most closely align to the end of the main scale, and this mark will give the reading of the rotating scale.
Let us now look at an example in which a micrometer is used to measure a length.
Example 2: Measuring a Length Using a Micrometer
What is the reading on the micrometer shown in the diagram?
The diagram shows the main scale and rotating scale of the micrometer. To obtain the reading on the micrometer, we need to record the reading on the main scale and on the rotating scale.
The main scale is the horizontal line. We can see that this consists of large numbered marks separated by small unnumbered marks. The large marks are 1 mm apart and the small marks are 0.5 mm apart from the large marks on either side of them.
We can see that the main scale reading is between 2.5 mm and 3 mm.
The rotating scale is the vertical line. It is not possible to see the entire rotating scale when looking at a micrometer in profile, as the scale is actually a circle rather than a vertical line, and half of the scale covers the unseen side of the thimble.
The full number of marks on the rotating scale is in fact 50. Turning the thimble sufficiently to change the main scale reading by 0.5 mm rotates the thimble through a complete revolution, leaving the reading on the rotating scale the same before and after the rotation.
The length corresponding to one mark on the rotating scale is given by
This is the smallest length that a micrometer can measure. It is important to understand that this is not a length equal to 1 micrometre (1 μm); rather, it is equal to 10 μm.
We can see that the mark on the rotating scale that most closely aligns to the main scale is the 25th mark.
The full reading on the micrometer is given by
Let us now look at an example involving comparing the accuracy of measurement tools for measuring length.
Example 3: Comparing Tools for Measuring Length
Which of the following tools is the most accurate tool for measuring length?
The tools shown are a micrometer, a tape measure, a ruler, and a vernier caliper.
The accuracy of a measurement corresponds to how close the measured value is to the real value of the quantity measured.
An important difference between the tools shown is the smallest length that each can measure.
Consider a length measured using a ruler as shown in the following figure.
The measured value of the length is 1.1 cm or 11 mm. We can see, however, that the length of the object is greater than the measured length. A measuring tool that could measure the fraction of a millimetre by which the length of the object exceeds 11 mm would have a value closer to the length of the object. The tool that can measure the smallest length is therefore the most accurate tool for measuring length.
Rulers and tape measures both measure minimum lengths of 1 mm, while vernier calipers and micrometer can measure lengths of less than 1 mm.
Vernier calipers can measure a minimum length of 0.1 mm. Micrometers can measure a minimum length of 0.01 mm.
The most accurate length measuring tool is therefore a micrometer.
Let us now look at an example that involves other measuring tools than rulers, vernier calipers, and micrometer.
Example 4: Identifying the Quantity Measured by Different Tools
Which of the following physical quantities can be measured by an hourglass, a pendulum clock, and a digital stopwatch?
The terms “clock” and “watch” applied to objects are familiar to most people, who would recognize that these refer to objects that give readings of time. The term “hourglass” contains the word “hour” which is a unit of time. Time is a physical quantity.
An object that gives a reading of time can be read at two different instances to measure the time that passes between the instances.
Mass is an SI base quantity. Mass is often confused with the SI-derived quantity “weight.”
Measuring devices that give readings in grams or kilograms, and so seem to be measuring mass, are in fact measuring weight.
Supposing that such a device was taken to the moon and used to measure the mass of the same object on the moon as on Earth, the result of the measurement would be different, but the mass of the object would actually be the same either on Earth or on the moon.
Tools that measure weight can be calibrated to give readings of mass, and then they will correctly read the mass of an object on Earth.
A tool that can measure weight is shown in the following figure. The arrow shows the direction of the weight that acts.
The action of the weight of a measured object extends the spring in the balance. The length of the spring is used to give a reading of weight.
Another such tool is shown in the following figure.
For a pan balance, two weights act, one on each pan. The pan balance compares these weights. The weight on one pan is produced by an object of a known mass.
Let us now look at an example involving such tools.
Example 5: Comparing Tools for Measuring Related Quantities
A beam balance, a spring balance, and a digital scale are types of measurement tools.
Which of the following physical quantities is typically measured by a beam balance and by a digital scale?
Which of the following physical quantities is typically measured by a spring balance?
Balances and scales do not measure length or time, so the answer to each part of the question is either mass or weight. All these tools actually measure weight but can be calibrated to give readings of mass or of weight.
Beam balances compare the weight of an object to that of another object, often a standard mass. Beam balances are usually calibrated to read mass measurements. Digital scales are also usually calibrated to read mass measurements. Spring balances measure the extension of a spring by an object suspended from the spring. This extension is more intuitively obvious as being due to the weight of an object, and spring balances are usually calibrated to read weight measurements.
Let us now summarize what has been learned in this explainer.
- Different tools are used to measure different physical quantities.
- Lengths of less than 1 millimetre can be measured by vernier calipers and by micrometer.
- A tool that gives a reading of time can be read at two different instances to measure the time that passes between the instances.
- Tools for measuring mass actually measure weight but can be calibrated so that if used on Earth they read the mass of objects.