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Physical Quantities

  Quantity Definition Formula Units Dimensions
Basic Mechanical Length or Distance fundamental d m (meter) L (Length)
Time fundamental t s (second) T (Time)
Mass fundamental m kg (kilogram) M (Mass)
Area distance2 A = d2 m2 L2
Volume distance3 V = d3 m3 L3
Density mass / volume d = m/V kg/m3 M/L3
Velocity distance / time v = d/t m/s
c (speed of light)
L/T
Acceleration velocity / time a = v/t m/s2 L/T2
Momentum mass × velocity p = m·v kg·m/s ML/T
Force
  Weight
mass × acceleration
mass × acceleration of gravity
F = m·a
W = m·g
N (newton) = kg·m/s2 ML/T2
Pressure or Stress force / area p = F/A Pa (pascal) = N/m2 = kg/(m·s2) M/LT2
Energy or Work
  Kinetic Energy
  Potential Energy
force × distance
mass × velocity2 / 2
mass × acceleration of gravity × height
E = F·d
KE = m·v2/2
PE = m·g·h
J (joule) = N·m = kg·m2/s2 ML2/T2
Power energy / time P = E/t W (watt) = J/s = kg·m2/s3 ML2/T3
Impulse force × time I = F·t N·s = kg·m/s ML/T
Action energy × time
momentum × distance
S = E·t
S = p·d
J·s = kg·m2/s
h (quantum of action)
ML2/T
Rotational Mechanical Angle fundamental θ ° (degree), rad (radian), rev
360° = 2π rad = 1 rev
dimensionless
Cycles fundamental n cyc (cycles) dimensionless
Frequency cycles / time f = n/t Hz (hertz) = cyc/s = 1/s 1/T
Angular Velocity angle / time ω = θ/t rad/s = 1/s 1/T
Angular Acceleration angular velocity / time α = ω/t rad/s2 = 1/s2 1/T2
Moment of Inertia mass × radius2 I = m·r2 kg·m2 ML2
Angular Momentum radius × momentum
moment of inertia × angular velocity
L = r·p
L = I·ω
J·s = kg·m2/s
ћ (quantum of angular momentum)
ML2/T
Torque or Moment radius × force
moment of inertia × angular acceleration
τ = r·F
τ = I·α
N·m = kg·m2/s2 ML2/T2
Thermal Temperature fundamental T °C (celsius), K (kelvin) K (Temp.)
Heat heat energy Q J (joule) = kg·m2/s2 ML2/T2
Entropy heat / temperature S = Q/T J/K ML2/T2K
Electromagnetic Electric Charge +/- fundamental q C (coulomb)
e (elementary charge)
Q (Charge)
Current charge / time i = q/t A (amp) = C/s Q/T
Voltage or Potential energy / charge V = E/q V (volt) = J/C ML2/QT2
Resistance voltage / current R = V/i Ω (ohm) = V/A ML2/Q2T
Capacitance charge / voltage C = q/V F (farad) = C/V Q2T2/ML2
Inductance voltage / (current / time) L = V/(i/t) H (henry) = V·s/A ML2/Q2
Electric Field voltage / distance
force / charge
E = V/d
E = F/q
V/m = N/C ML/QT2
Electric Flux electric field × area ΦE = E·A V·m = N·m2/C ML3/QT2
Magnetic Field force / (charge × velocity) B = F/(q·v) T (tesla) = Wb/m2 = N·s/(C·m) M/QT
Magnetic Flux magnetic field × area ΦM = B·A Wb (weber) = V·s = J·s/C ML2/QT

Note: Other conventions define different quantities to be fundamental.

Mass, energy, momentum, angular momentum, and charge are conserved, which means the total amount does not change in an isolated system.


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Keith Enevoldsen's Think Zone