A. Physical Quantities

  

Physical quantities is a physical property of a phenomenon, body, or substance, that can be quantified by measurement. A physical quantity can be expressed as the combination of a magnitude expressed by a number and a unit. There are two types of quantities; base quantities and derived quantities. 

 Base quantities are fundamental physical quantities that are not defined in terms of other physical quantities.

The seven base quantities of the International System of Quantities (ISQ) and their corresponding SI units and dimensions are listed in the following table.

 

               

The base quantities have the following characteristics:

1.    They are not derivations of other quantities. 

2.    They can produce or derive other quantities.

    Derived quantities are the derivations or combinations of the base quantities. 

 Here are some example of derived quantities:

    



B. Unit and Dimension

  Unit is a quantity used as a standard of a measurement. Unit helps us to know the exact quantity of the measurement result. 

Let's take an example!

Annie went to the market last Thursday. There, the seller how much sugars she needed. She said, "I need 5 rice, please!" Of course, by saying that Annie has made the seller confused. But if she said," I need 5 kg of rice, please!", the seller could directly give it to her without being confuse.

 Why this thing could happen? It's because unit states an exact value as the standard of things. By saying kg, the seller will understand that she need 5 kilos instead of 5 pieces of rice.

Units among every countries are different. Indonesia uses rupiah, Malaysia uses ringgit, and some others. In order to make an effective way for the economic circulation among countries, scientists created an International system of units. The SI units is units on the base quantities.

Dimension is an expression of the character of a derived quantity in relation to fundamental quantities, without regard for its numerical value. 

Dimensional analysis is useful method for determining the units of a variable in an equation.

Generally, the dimension of a physical quantity is symbolized by square parenthesis "[]".

 The function of dimensional analysis:

• Dimensional equations are used to validate the correctness of a physical equation.

• Dimensional equations are used to derive correct relationship between different physical quantities.

• Dimensional equations are used to convert one system of units to another.

• Dimensional equations are used to find the dimension of a physical constant.

 The base dimensions are:

The dimensional formula are like these:

C. Measurement

Measurement is a process of comparing the magnitude of a physical quantity with the values which belong to a measuring devices.

 There are 2 ways in doing measurement:

1) Single measurement

 Using this formula:

2) Repeatedly measurement

Below is the example of the measurement:

                   

The formula: 

 

              

To report the result, we use this formula:

Some measuring devices are:

Vernier caliper

 

A caliper can be used to measured with a precision of 0.1mm. Consequently, the uncertainty of measurement using this caliper is the half value of 0.1 mm, which is 0.05 mm. To measure by using caliper, you should make the addition of main scale and nonius scale. The main scale is surpassed by the zero scale of nonius.  A caliper can be used to measure the diameter of a thing. 

Micrometer

 A micrometer is used to measure with a precision of 0.01 mm which is more precise than caliper. Just like the caliper, you need to sum up the main scale of the nonius scale.

The uncertainty of the micrometer is 0.005 mm

Uncertainty

Uncertainty greatly affects the accuracy of the measurement. The uncertainty may occur when the equipment is incorrectly set or has never been calibrated. 

Relative Uncertainty

Sometimes we need to know how large an uncertainty of measurement is compared to the measured value. We then define a relative uncertainty as a fraction of uncertainty to the measured value as expressed in the following equation:

Every measuring device has its uncertainty value. For, micrometer and caliper they have their own uncertainty value which is unchangeable. Here are the formula of the uncertainties measurement of the micrometer and caliper:

* The example is on the result report of the repeatedly measurement, but the uncertainty is depend on the measuring device.

D. Significant Figure

Significant figure are the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.

Significant figure rules:

• Any digit that is not zero is significant. Thus 642 has three significant figures and 6.792 has four significant figures.
• Zeros between non zero digits are significant. Thus 4023 has four significant figures.
• All numbers in scientific notation are significant figure. Thus 7.2 x10^-5 has 2 significant figures
• Leading zeros are not significant.  Thus, 0.00005 has 1 significant figure
• Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0. 
• Trailing zeros in a number that dont contain a decimal point are significant. Thus 500 has 1 significant figure. 

Multiplication and Division

The rule of the multiplication and division is still connect to significant figure term. In the multiplication and division, the result of them is depend on the smallest significant figures.

For example: