**FUNDAMENTAL AND DERIVED UNITS :**

In mechanics, there are three basic units or fundamental units and they are length, time and mass. Derived units are then represented where dimensional representatives are necessary.

**FUNDAMENTAL UNITS**

Fundamental unit are the basic foundational units in science and there are a few of this fundamental physical quantities.

**DERIVED UNITS **

This simply is the combination of the fundalmental unit. From the combination of one of the same or two or more fundalmental units we can obtain other useful units. Such units are called derived units.

The unit of volume is obtained by multiplying three lengths, which is called cubic meters. Density is the ratio of mass and volume. Then the S.I. unit of density is called kilogram per cubic meter.

Speed is the ratio of distance and time, so therefore the unit is called meter per seconds. Other derived units are listed below:

**Examples**:

Note that in dimensions,

i. Mass is represented by letter “M”

ii. Time is represented by letter “T”

iii. Length or distance is represented by letter “L”

**Simple Calculations of some Dimensions**

These are the three major symbols used in dimension. So let’s see how it is use in dimensioning;

**FORCE**: This is the product of mass and acceleration

F = ma

Where: m = mass = M

a = acceleration = L/T² ..…………… (i)

So the dimension for Force = M L/T²

**MOMENTUM**: This is the product of mass and velocity

P = MV

Where: m = mass = M

V = Velocity = L/T ………………………. (ii)

So the dimension for Momentum is = ML/T

**PRESSURE**: This is force per unit area

Where: F = force = as in (i) above

A = area = L² ….……………. (iii)

So the dimension for Pressure is = F / A

= M L/T² * 1/ L² = M/ T² L

**VOLUME**: is the quantity of three-dimensional space enclosed by some closed boundary.

V = L³………………………. (iv)

**DENSITY**: This is mass per unit volume

Where: M = mass = M

V = volume = L³………………. (v)

The dimension for Density is = M/ L³

**VELOCITY**: This is distance per unit time

Where: D = Distance = L

T = Time = T …………………………. (vi)

The dimension for velocity is = L/T

**ACCELERATION**: This is velocity per unit time

Where: V = velocity = as in (vi) above

T = time = T …………………………… (vii)

The dimension for acceleration is = V/T = L/T * 1/T

= L/ T²

**IMPULSE**: This is the product of force and time

Where: F = force = as in (i) above

T = time = T ……..………… (viii)

The dimension for impulse is = F * T

= M L/T² * T

= ML/T

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