UniT & measurements 

Physics is an experimental science and experiments require measurement of physical quantities. Measuring a physical quantity involves comparing the quantity with a reference standard called the unit of the quantity. 

Some physical quantities are taken as base quantities and other quantities are expressed in terms of the base quantities called derived quantities. This forms a system of base quantities and their units. 

Without performing proper measurements we cannot describe the physical phenomena quantitatively. 

To measure a physical quantity we need some standard unit of that quantity. The measurement of the quantity is mentioned in two parts, 

• The first part gives magnitude 

• The second part gives the name of the unit 

Example,

Length of this wire is 5 meters. 

The numeric part 5 says that it is 5 times of the unit of length and the second part meter says that unit chosen here is meter. 

The imperial system is a measurement system that includes units such as inches, feet, pounds, and gallons, originating from the British Empire. It is also referred to as the British Imperial system or imperial units. Although most countries have adopted the metric system, the United States, Liberia, and Myanmar continue to primarily use the imperial system. 

📐CGS System (Centimeter, Gram, Second) : 

In this system, 

The unit of Length is the centimeter 

The unit of mass is the gram  

The unit of time is the second  

⚓ FPS System (Foot, Pound, Second) :

In this system, 

The unit of length is the foot 

The unit of mass is the pound 

The unit of time is the second 

🚏 MKS System (Meter, Kilogram, Second) : 

In this system, 

The unit of length is the meter  

The unit of mass is the kilogram  

The unit of time is the second 

The SI system consists of seven fundamental units and two supplementary units (radian and steradian) that measure plane and solid angles, respectively. 

The basic physical quantities, which are independent of other quantities, are known as the fundamental quantities. 

For example, mass, length and time are considered to be the fundamental quantities. In the same manner, the units which can be derived from the fundamental units are known as derived units. In mechanics, virtually all quantities can be expressed in terms of mass, length and time. 

We now provide these basic seven quantities with their units and symbols: 

Derived units are those that can be expressed in terms of fundamental units. Every derived unit is originated from some physical law defining that unit. These units are essential for measuring more complex physical quantities. There are several steps involved in deriving a unit. 

Step -1 : Identify the formula for the quantity.

Step -2 : Substitute the units of all involved quantities in the same system.

Step -3 : Simplify the expression to obtain the final derived unit. 

• Derived units are created by combining fundamental units, allowing for the measurement of more specific physical phenomena like velocity, force, and energy.

• Derived units can be expressed through mathematical formulas, making them versatile for a wide range of scientific and engineering applications .

📏 Unit of every physical quantity should be represented by its symbol.

🧑‍🔬 Full name of a unit always starts with smaller letter even if the name is after a person, e.g., 1 newton, 1 joule, etc. 

⚖️But symbol for unit named after a person should be in capital letter, e.g., N after scientist Newton, J after scientist Joule, etc. 

🏗️ Symbols for units do not take plural form 

e.g., force of 20 N and not 20 newtons or not 20 Ns. 

🙅‍♂️ Symbols for units do not contain any full stops at the end of recommended letter 

e.g., 25 kg and not 25 kg.

➗The units of physical quantities in numerator and denominator should be written as one ratio 

e.g., the SI unit of acceleration is m/s2 or m s-2 but not m/s/s. 

All the physical quantities of interest can be derived from the base quantities. Thus, when a quantity is expressed in terms of the base quantities, it is written as a product of different powers of the base quantities. Further, the exponent of a base quantity that enters into the expression is called the dimension of the quantity in that base. To make it clear, consider the physical quantity ”force”. As we shall learn later, force is equal to mass times acceleration. 

We know that acceleration is change in velocity divided by time interval but velocity is length divided by time interval.  

Dimensional analysis is the use of a set of units to establish the form of an equation, or more often, to check that the answer to a calculation as a guard against many simple errors.