Units and Dimensions - Introduction

Description:

Units

• Units are the most basic aspect of any measurement.
• They are arbitrarily chosen and internationally accepted.

For example, the picture below is of the platinum rod, whose length is the standard for 1 m in the world.

Units are categorized in the following ways −

Fundamental Units

• Some units are arbitrarily chosen to be fundamental.
• They become the foundation for the system.
• Every other unit is derivable from them.

Derived Units

• Units derived from the fundamental units by multiplication and division are called derived units.

E.g. If speed and time are fundamental quantities, then,

Length = Speed × Time

Length becomes a derived quantity. It is obtained by multiplication of two fundamental quantities.

However, if length and time are fundamental quantities, then,

Speed = Length/Time

Speed becomes a derived quantity. It is obtained by division of two fundamental quantities.

Earlier System of Units

CGS System (Three fundamental quantities)

• Centimetre for Length
• Gram for Mass
• Second for Time

FPS System (Three fundamental quantities)

• Foot for Length
• Pound for Mass
• Second for Time

MKS System (Three fundamental quantities)

• Meter for Length
• Kilogram for Mass
• Second for Time

SI System

At present, the system of units accepted internationally is the SI system. SI System has seven base (fundamental) units and two other base units.

Plane Angle

Plane Angle (dθ) is defined as the ratio of length of arc ‘ds’ (small section) to the radius r. Unit for plane angle is Radians (rad).

Above diagram shows a sector (of a circle) with the small angle ‘dθ’ at the center. It is defined as follows −

dθ = ds/r

One can get an intuitive understanding by making the angle at the center equal to 2π radians.

Now we have learnt in lower standards that the circumference of a circle is equal to 2πr.

The same can be interpreted using the definition of the plane angle,

Circumference = S = r × θ

S = 2πr

Solid Angle

Solid Angle (dΩ) is the ratio of intercepted area ‘dA’ (small section) to the radius r². Unit for plane angle is Steradians (sr).

Above picture shows a solid sector cut out of a solid sphere. Analyzing this sector,

Here, ‘dΩ’ is the solid angle subtended at the center. It is defined as follows −

dΩ = dA/r²

One can get an intuitive understanding by making the angle at the center equal to 4π steradians.

We have learnt in lower standards that the circumference of a circle is equal to 4πr².

This can be interpreted using above definition of the solid angle,

A = Ω × r²

A = 4πr²

Where, ′A′ is the total surface area of the sphere.

Prefixes to the units

Prefixes for negative powers of 10.

Examples −

1.1 nm = 1.1 nanometers = 1.1×10⁻⁹ m

2.3 mmol = 2.3 millimoles = 2.3×10⁻³ mol

Prefixes for positive powers of 10.

Examples −

1.1 Tm = 1.1 Terameters = 1.1×10¹² m

2.3 GK = 2.3 Gigakelvin = 2.3×10⁹ K