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.

Physical Quantities and SI units

Measurement is an important part of physics. In physics, we are especially concerned with what standars of reference are used and how accurate the measurements are.

A physical quantity is a quantity that can be measured. It consists of a numerical magnitude and a unit. They are found on signboards and labels almost everywhere in our daily lives.

Altogether, there are seven basic physical quantities, or base quantities. Length and Time are two of them. Listed here are the seven basic physical quantities

• Base Quantity : Length                            Name of SI unit : Metre        Symbol for SI unit : m
• Base Quantity : Mass                               Name of SI unit : Kilogram  Symbol for SI unit : kg
• Base Quantity : Time                               Name of SI unit : Second     Symbol for SI unit : s
• Base Quantity : Electric Current              Name of SI unit : Ampere    Symbol for SI unit : A
• Base Quantity : Thermodynamic Temp   Name of SI unit :  Kelvin     Symbol for SI unit : K
• Base Quantity : Luminous Intensity        Name of SI unit : Candela    Symbol for SI unit : cd
• Base Quantity : Amount of substance     Name of SI unit : mole         Symbol for SI unit : mol

The units of these seven base quantities are known as SI units, from the French Le Systeme International d'Unites. The five that we have to learn are length, mass, time, electric current and temperature.

Other common physical quantities such as area, volume and speed are derived from these seven quantities. That is why these are called derived quantities. e.g. Speed is derived from length and time.

Area is derived from length and width. Volume is derived from length, width and height. 

The reason as to why we need SI units was because in the past, people used parts of their bodies and things around them as units of measurement. Thats how measuring terms like foot, yard and horsepower came about. However, these units of measurement caused much confusion as they varied from person to person. In 1968, scientists decided to adopt one universal set of units - the SI units

Using decimal notation, the distance between air molecules would be represented as 0.00000001m. It would be both tiring and confusing if we needed to mention this a few times. The more convenient thing to do would be to use prefixes to represent the above quantity. In this case it can be represented as 0.01µm (micrometre) where µ represents the submultiple 10-6. The prefixes listed below are very useful in expressing physical quantities that are either very big or very small. There is another way to express the same quantity (0.01µm) and that is to use the standard form. In this case, it will be expressed as 1 x 10^-8 m.

It takes some time to memorize this table completely. However, there are still a few more common quantities that are expressed in standard form

• One Kilometre (km)           1 x 10³ m
• One Milliampere (mA)       10^-3 A
• Three Megajoules (MJ)       3 x 10⁶  J
• Six Microcoulombs (µC)    6 x 10^-6  C
• Eight Nanoseconds (ns)      8 x 10^-9 s

What Is Physics?

Physics is the study of the natural world around us - from the very large, such as the Solar System, to the very small, such as the atom.

I made a concept map addressing the ideas we may approach while studying Physics.

                      

                    

As you can see above, the study of Physics is divided into 4 major topics which are General Physics, Thermal Physics, Light, Waves & Sound and Electricity & Magnetism. 

We must remember that the knowledge of Physics we have today is the result of work of MANY scientists over centuries. These scientists built and tested their ideas on matter and energy, and verified their ideas or theories by doing experiments. 

When we do experiments, it is crucial that we take measures to ensure reliable and accurate results. Accurate measurement is of utmost importance.