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Derived Quantities and SI units

Derived Quantity Unit Symbol Base unit combination

Force newton N kg m s^-2

Pressure pascal Pa kg m^-1 s^-2

Energy joule J kg m² s^-2

Power watt W kg m² s^-3

Electric Charge coulomb C A s

Electric Potential volt V kg m² s^-3 A^-1

Electrical Resistance ohm W kg m² s^-3 A^-2

Electrical Conductance siemens S kg^-1 m^-2 s³ A²

Capacitance farad F kg^-1 m^-2 s⁴ A²

Mag. Flux Density tesla T kg s^-2 A^-1

Activity bequerel Bq s^-1

Derived Quantity	Unit	Symbol	Base unit combination
Force	newton	N	kg m s^-2
Pressure	pascal	Pa	kg m^-1 s^-2
Energy	joule	J	kg m² s^-2
Power	watt	W	kg m² s^-3
Electric Charge	coulomb	C	A s
Electric Potential	volt	V	kg m² s^-3 A^-1
Electrical Resistance	ohm	W	kg m² s^-3 A^-2
Electrical Conductance	siemens	S	kg^-1 m^-2 s³ A²
Capacitance	farad	F	kg^-1 m^-2 s⁴ A²
Mag. Flux Density	tesla	T	kg s^-2 A^-1
Activity	bequerel	Bq	s^-1

Standard Prefixes

Multiple Prefix Symbol

10³ kilo K
10⁶ mega M
10⁹ giga G
10¹² tera T
10¹⁵ peta P
10¹⁸ exa E

Submultiple Prefix Symbol

10^-3 milli m
10^-6 micro µ
10^-9 nano n
10^-12 pico p
10^-15 femto f
10^-18 ato a

Multiple	Prefix	Symbol
10³	kilo	K
10⁶	mega	M
10⁹	giga	G
10¹²	tera	T
10¹⁵	peta	P
10¹⁸	exa	E

Submultiple	Prefix	Symbol
10^-3	milli	m
10^-6	micro	µ
10^-9	nano	n
10^-12	pico	p
10^-15	femto	f
10^-18	ato	a

Homogeneity of Equations

The kinetic energy (E_k) of a moving body of mass (m) moving with velocity (v) is given by:

E_k = 1/2mv²
Taking each term in turn:
units of E_k : kg m² s^-2

units of 1/2mv²: kg * (ms^-1)² = kg m² s^-2

(The factor 1/2 is a pure number and has no units)

Scalar and Vector quantities

Vector quantities are those which have both magnitude (size) and direction. Those with only magnitude are called scalars

Examples of Scalar and Vector quantities

Scalars Vectors

length,area,volume,speed,time,mass,density, pressure,energy,power,temperature,electric charge,electric potential displacement,velocity,acceleration,force, weight,momentum,torque,electric current,electric field strength,magnetic field strength

Scalars	Vectors
length,area,volume,speed,time,mass,density, pressure,energy,power,temperature,electric charge,electric potential	displacement,velocity,acceleration,force, weight,momentum,torque,electric current,electric field strength,magnetic field strength

This is a nice example of vector quantity use. The case is that of examining a cross wind at 90º to the aircrafts velocity. Pythagoras gives us the magnitude of resultant velocity

vr=(20²+40²)^1/2=44.7ms^-1
and using trigonometry to find direction:
α=tan^-1(20/40)=26.6º East of North

Physical constants and units

Constant	Symbol	Value
acceleration due to gravity	g	9.81 m s^-2
Gravatational Constant	G	6.673*10^-11Nm²kg^-2
Avogadro constant	N_A	6.023*10²³mol^-1
Ice point	T_ice	273.15K
Gas constant	R	8.314JK^-1mol^-1
Boltzmann constant	k	1.381*10^-23JK^-1
Stefan constant	σ	5.670*10^-8Wm^-2K^-4
Rydberg constant	R_hc	1.097*10⁷m^-1
Planck constant	h	6.626*10^-34Js
Speed of light in vaccum	c	2.998*10⁸ms^-1
Charge of proton	e	1.602*10^-19C
Mass of electron	m_e	9.109*10^-31kg
Rest energy of electron	E_e	0.511MeV
One atomic mass unit	u	1.66*10^-27kg
Atomic mass unit energy equivalent		931.5MeV
Electric constant	ε₀	8.854*10^-12Fm^-1
Magnetic constant	μ₀	4π*10^-7Hm^-1
Bohr magneton	μ_B	9.274*10^-24Am²
Nuclear magneton	μ_N	5.051*10^-27Am²
Fine structure constant	α	7.297*10^-3
Compton wavelength of electron	λ_c	2.426*10^-12m
Bohr radius	a₀	5.2918*10^-11m
Angstrom	Ǻ	10^-10m
torr	torr	133.32Pa
barn	b	10^-28m²