ENGINEERING MECHANICS - Lecture Note

PHYSICAL QUANTITIES, UNITS AND UNIT SYSTEMS

PHYSICAL QUANTITIES

A property which can be measured or quantified
It can be represented as a number and a corresponding unit

UNITS

A unit is usually mentioned along with the measured physical quantity expressed in numbers. This distinguishes different physical quantities.

> Fundamental units are those which cannot be expressed in terms of other quantities and have physical independence of their own

> 7 fundamental units are:

> 2 supplementary quantities are:

> Derived units: All other units which can be expressed in terms of fundamental units.

Example:

Area m²

Volume m³

Density kg/m³

Velocity m/s

Acceleration m/s²

Force Newton = 1 kg m/s²

Stress, pressure F/A = N/m²= Pascal

Moment Fxr = Nm

Work, energy F x s = Nm=Joule

> A vector is often represented by an arrow pointing in the direction of quantity

Eg., Force vector of magnitude 5N is expressed in X direction as F_x = 5i N (where i is a vector of magnitude 1 in the x direction.)

Dimensional Formula

> Method of expressing a physical quantity in terms of fundamental quantities with proper manner

UNIT SYSTEMS

1. CGS system of units [Centimeter-Gram-Second]

Length ———-> cm
Mass ————> gram
Time ————>second
Force————>dyne
Speed———–>kyne
Acceleration —->gal
Energy———–>erg
Power————>erg/s

2. FPS system of units [Foot-Pound-Second]

Length ———–>foot
Mass ————->pound
Time ————->second
Force ————>poundal
Energy ———–>poundal-foot
Power ————>horse power

3. MKS system of units [Meter-kilogram-second]

Length ————>meter
Mass ————–>kilogram
Time ————–>second
Force ————->newton kgf
Energy ————>joule
Power ————->watt
Pressure ———->Pascal

4. SI system of units

> French – system international d/ unites (International system of units)

> Adopted in 1960 by the General conference on weight and measures

Length ——————->meter
Mass ———————>kilogram
Time ———————>second
Force ——————–>Newton
Energy ——————->Joule
Power ——————–>Watt
Pressure —————–>Pascal
Capacitance ————->Farad
Electric charge ———–>Coulomb
Electric conductance —–>Siemens
Magnetic conductance —>Henry
Electric potential ———->Volt
Electric resistance ———>Ohm
Illuminance —————->Lux
Luminous flux ————–>Lumen
Magnetic flux ————–>Weber
Magnetic flux density ——>Tesla
Plane angle —————->Radian
Solid angle —————–>Steradian

BASIC TRIGONOMETRY

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