Measurement and Units Revision

Fundamental Quantities and Base Units

In science there are five fundamental quantities, or base quantities. All other quantities, called derived quantities, are related to these five base quantities.

To measure a physical quantity we compare it with a standard known as the unit, called base unit, of the quantity. 

A quantity is written as its value followed by its unit, e.g. the height of the girl is 1.40 m. This system of units we use is called the Systeme International d'Unites (International System of Units) or in short, the SI system.

Derived Quantities

We can multiply or divide base quantities with their units to produce derived quantities with their units. For example, the area of a rectangle with sides 0.6 m and 0.5 m  is given by the product of its sides, i.e. (0.6 m) x (0.5 m) = 0.3 m²

Remember in algebra that y  X  y = y²

Similarly, metre x metre equals metre squared, i.e. m  X  m  = m²

Length

Length can be measured using various instruments. You can use a ruler to measure to the nearest millimetre. However, a ruler is not suitable for measure very short distances, such as the diameter of a wire or the thickness of a sheet of paper. In these cases, a micrometre screw gauge or calipers are used.

Micrometer Screw Gauge

The main scale is marked in millimetres (mm). As the screw rotates once the micrometre opens 0.5 mm. Each of the 50 divisions on the rotating scale is 0.01 mm. A micrometre screw gauge can be used to measure the diameter of a wire and even the diameter of the human hair. If you have forgotten how to read a micrometer screw gauge check your textbook. Also, you can come to me for any help.

Vernier Callipers

The vernier calliper can also be used to measure the diameters of objects. It has a main scale and a vernier scale. The vernier scale can slide along the main scale. Read up on how to use the vernier scale. Again, if you need assistance, you can contact me.

Area

The area of a rectangle is the product of the lengths of the sides.
 

Remember the formula: Area = length x width

With irregular shapes we can divide the area into small squares, of known size, and estimate the total number of squares.

Volume

To find the volume of rectangular solids (cuboids) we measure the lengths of the sides. Remember the formula: volume = length x width x height

For irregular solids another method is employed. We simply immerse the object into water. The volume of water displaced is equal to the volume of the object.

In the above example, the volume of the stone is 100cm³

For larger irregular objects, the eureka can method (displacement can method) is used. The volume of the object is equal to the volume of water that overflows. 

The volume of liquids is found by using a measuring cylinder and looking carefully at the bottom of the meniscus. Pipettes and burettes can also be used.

Mass

To measure mass balances are used. There are different types of balances: lever balance, triple beam balance, and chemical balance. The scale on a lever arm balance is non-linear, i.e. the marks are not evenly spaced. Note that mass and weight are different.

Density

Density can be defined as the mass per unit volume of a substance. Blocks of materials can have the same volume but different masses. A wooden block may have a mass of 48g while a block of iron of the same volume has a mass of about 420g. This is because the materials have different densities.

Remember the formula for density is mass divided by volume and its unit is kilogram per metre cubed, i.e.  Kg m^-3

Relative Density

Relative density is the comparison of the density of a material with the density of water. It is found by dividing the density of the substance by the density of water. Relative density is a ration and it has no units.

Time

A stopwatch or stop clock is used to measure intervals of time. Your reaction time causes inaccuracy but you can increase the credibility of your results by repeating timings and averaging your results.