Measurement of Length

In Physics, length is an important quantity that is measured almost all the time. For example, we measure length to know how far an object has moved, how much space an object occupies or how far apart two objects are.

The SI unit for length is metre(m). There is a wide range of lengths in this world. It is crucial that we use the appropriate instruments and methods to measure different types of length. The metre rule and tape measure are two examples of instruments that can be used.

The metre rule and tape measure are common instruments used to measure length. A metre rule can measure lengths up to one metre. Suppose we want to measure a pond which is about 10m. Which measuring instrument would we use?

We would most probably use a retractable steel tape. The retractable steel tape should be long enough to measure the distance. How about measuring the depth of the pond? A metre rule would be used.

What is the smallest unit on the metre rule? It is 0.1cm or 1mm. The smallest unit an instrument can measure is known as its "precision". For example, the metre rule cannot accurately measure the thickness of a piece of paper, which is obviously thinner than 1mm. You will have to estimate its thickness. In this case, the uncertainty, known as the instrument error, is due to the limitations of the metre rule.

When reading the metre rule, we must position our eye directly above the markings to avoid parallax errors. By taking several readings and taking the average, you will minimize reading errors. 

The zero mark on a metre rule is often at the very end of it. Wear and tear may make the mark unsuitable for measuring purposes. The worn end may introduce errors to the readings. Hence it is better to measure from some randomly chosen point and subtract it from the final reading. 

An instrument for measuring the diameters of cylinders or circular objects are the calipers. The jaws of the calipers are used to grip the widest part of the object. When the object is removed, the distance between the jaws can be measured using a metre rule. By inverting the jaws of the calipers, inner diameters can also be measured. 

The vernier calipers consist of a main scale and a sliding vernier scale. It is a useful tool that is used to measure both the internal and external diameters of an object. The vernier calipers are able to measure to a precision of 0.01cm.

Parts of The Vernier Calipers

Inside Jaws      - used to measure the internal diameter of an object
Outside Jaws   - used to measure the external diameter or width of an object
Vernier Scales - a small sliding scale attached to the main scale that allows us to read a fraction of the smallest interval.
Tail                 - used to measure the depth of an object

Before using the vernier calipers, we need to examine the instrument for zero error. This is to check that the zero mark on the main scale coincides with the zero mark on the sliding vernier scale when we are not measuring anything between the jaws.

If the two zero marks coincide, there is no zero error.
If the zero mark on vernier is slightly to the right there is a positive zero error of +0.03cm. This means that we have to subtract 0.03cm from the reading. /e.g. 0.03/
If the zero mark on vernier is slightly to the left there is a negative zero error of -0.03cm. This means that we have to add it to the reading. /e.g. 0.03/

How to Use the Vernier Calipers

Step 1 : Grip the ball bearing gently using the outside jaws of the calipers.

Step 2 : Read the main scale directly opposite the zero mark on the vernier scale. 

Step 3 : Read the vernier mark that coincides with a marking on the main scale. 

Step 4 : The diameter is found by adding the main scale reading to the vernier scale reading.

The micrometer screw gauge is used to measure lengths to a precision of 0.01mm or 12 micrometers. It can measure the external diameter of wires and ball bearings. We use it mainly to measure anything less than 1cm - too mall for vernier calipers to measure.

How to Use the Micrometer Screw Gauge

Step 1 : Turn the thimble until the anvil and the spindle gently grip the object. Then turn the ratchet until it starts to click.

Step 2 : Read the main scale reading at the edge of the thimble. 

Step 3 : The thimble scale has 50 divisions, each of which is 0.01mm. Take the thimble reading opposite the datum line of the main scale. 

Step 4 : Diameter is found by adding the main scale reading to the thimble reading. 

If the two zero marks on the micrometer screw gauge coincides, there is no zero error.
If the zero mark on datum line is to the left, there is a positive zero error. We have to subtract it from the reading.
If the zero mark on datum line is to the right, there is a negative zero error. We have to add it to the reading.