Given in the table below are the fundamental units of measure for the Systeme Internationale - or the MKS metric system. Also shown is a second popular collection of units is called the CGS system.
These are the basic units from which all other metric units of measure are derived. For example:
Speed is a derived quantity that expresses how rapidly an object travels a given distance with respect to time. It is measured in m/sec.
(scalar) quantity: speed
(formula) variable: r
units of measure: m/sec
Presented below are the
most common derived units from mechanics.
This link will take you to a more complete summary of the formulas and units of measure used in standard introductory physics courses.
name | vector/scalar | variable | common formula | unit of measure | relationships |
length | scalar | L | | m | 1 m = 100 cm |
height | scalar | h | | m | |
area | scalar | A | A = L•w | m2 | 1 m2 = (100 cm)2 |
volume | scalar | V | V = L•w•h | m3 | 1 m3 = (100 cm)3 |
mass | scalar | m or M | | kg | 1 kg = 1000 g |
density | scalar | D | D = M / V | kg/m3 | 1 kg/m3 = 10-3 g/cm3 |
distance | scalar | d | | m | |
displacement | vector | s | | m | |
time | scalar | t | | sec | |
speed | scalar | r | r = d / t | m/sec | |
velocity | vector | v | v = s / t | m/sec | |
momentum | vector | p | p = mv | kg m/sec | |
acceleration | vector | a | a = Δv /Δt | m/sec/sec | m/sec2 |
gravity | vector | g | g = GME/RE2 | m/sec2 | 9.8 m/sec2 |
force | vector | F | F = ma | | |
MKS: kg(m/sec2) | nt, N (newton) |
CGS: g(cm/sec2) | dyne 1 N = 105 dynes |
tension | vector | T | | nt | strings, wires |
spring constant | scalar | k | F = ks | nt/m | |
impulse | vector | J | J = Δp = Ft | kg m/sec | nt sec |
pressure | vector | P | P = F / A | nt/m2 | Pa (Pascal) |
work | scalar | W | W = Fs | | |
MKS: kg(m2/sec2)
| nt m = J (Joule) |
CGS: g(cm2/sec2)
| erg 1 J = 107 ergs |
energy | scalar | E | W = ΔE | kg(m2/sec2) | nt m = J (Joule) |
gravitational potential energy | PEg = mgh | | |
elastic potential energy | PEe = ½ks2 | | |
kinetic energy | KE = ½mv2 | | |
power | scalar | P | P = W / t | | watt = J / sec |
frequency | scalar | f | f = #events / t | 1/sec | hz (hertz) |
period | scalar | T | T = 1 / f | sec | |
angle | scalar | θ | | ° or radians | 90° = π/2 rads |
torque | vector | τ | τ = FL⊥ | m nt | |
temperature | scalar | T | | K or °C | 0 K = -273°C |