We will distinguish between fundamental and derived units.
In IB Physics there are six fundamental units from which all others required can be derived.
Units can be used as a mechanism to check the possibility that an equation could exist.
Key Concepts
Fundamental units
These units are referred to as fundamental, which means they form the basis of all other derived units. These were agreed by scientists at a conference and, henceforth, known as the Systeme Internationale base units.
Quantity
Unit
Symbol
Length
meter
m
Mass
kilogram
kg
Time
second
s
Electric current
ampere
A
Temperature
kelvin
K
Quantity of substance
mole
mol
(Luminosity)
(candela)
(cd)
Note that the kilogram is the only fundamental unit with a unit prefix as standard.
Derived units
The units below are not base units; they can all be derived from the base units.
Quantity
Unit
Symbol
Plane angle
radian
rad
Frequency
hertz
Hz
Force
newton
N
Pressure
pascal
Pa
Energy
joule
J
Power
watt
W
Charge
coulomb
C
Potential
volt
V
Resistance
ohm
Ω
Capacitance
farad
F
Magnetic flux
weber
Wb
Magnetic flux density
tesla
T
Activity
becquerel
Bq
Conversions
Area: Square the unit prefix conversion factor
1 m2 = 104 cm2 = 106 mm2
Volume: Cube the unit prefix conversion factor
1 m3 = 106 cm3 = 109 mm3 = 1000 litres
Temperature
273 K = 0 °C
Angle
2π radian = 360°
Energy: There are several units of energy, each with an appropriate use
1 kcal = 4.4 kJ
1 kWh = 3.6 MJ
1 kilo Watt hour is the energy required to power a 1 W device for 1 hour (NB: energy = power x time)
1 eV = 1.6x10-19 J
1 electron volt is the kinetic energy gained by 1 electron accelerated through a potential difference of 1 volt (NB: energy = charge x potential difference)
Essentials
Dimensional analysis
The units for any quantity in mechanics can be expressed in terms of mass (M) length (L) and time (T).
Quantity
unit
Dimensions
velocity
m s-1
L T-1
acceleration
m s-2
L T-2
Force
N
M L T-2
Energy
J
M L2 T-2
Power
W
M L2 T-3
This video gives an example - the dimensional analysis of power.
Dimensional consistency
In any formula, the dimensions on the right of the equals sign must be the same as the dimensions on the left. This is also true for quantities being added or subtracted.