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 and the second part gives the name of the unit. Thus, suppose I say that 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, and 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, and 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, and 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 .

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.