Why all the variations? Some quantities have compound units that are made up of a combination of the base SI units. After carrying the units along in your calculations, sometimes it’s not obvious if you’ve ended up with the correct units, so this puts each compound unit side by side with the “unzipped” version of itself. I hope this helps you when working with units!

Note: If you are viewing on a phone or tablet, it will be easier to read if you rotate into landscape so that the units will appear next to the variables instead of below them.

Translational

Rotational

Displacement

   r⃗, x, y, z \Large \mathrm{\, \, \, \vec{r}, \, x, \, y, \, z}
[m] \mathrm{[m]}
θ \Large \mathrm{\theta}
[radians] or [rad] \mathrm{[radians] \, or \, [rad]}

Speed/Velocity

v⃗ \Large \mathrm{\vec{v}}
[ms] \Large \mathrm{[ \frac{m}{s}]}
ω⃗ \Large \mathrm{\vec{\omega}}
[rads] \Large \mathrm{[\frac{rad}{s}]}

Acceleration

a⃗ \Large \mathrm{\vec{a}}
[ms2] \Large \mathrm{[\frac{m}{s^2}]}
α⃗ \Large \mathrm{\vec{\alpha}}
[rads2] \Large \mathrm{[\frac{rad}{s^2}]}

Force

Torque

F⃗ \Large \mathrm{\vec{F}}
[N] or [kg⋅ms2] \mathrm{[N] \, or \,} \Large \mathrm{[\frac{kg \cdot m}{s^2}]}
τ⃗ \Large \mathrm{\vec{\tau}}
[N⋅m] \mathrm{[N \cdot m]}

Mass

Rotational Inertia

m \Large \mathrm{m}
[kg] \mathrm{[kg]}
I \Large \mathrm{I}
[kg⋅m2] \mathrm{[kg \cdot m^2]}

Linear (Translational) Momentum

Angular Momentum

p⃗ \Large \mathrm{\vec{p}}
[kg⋅ms] \Large \mathrm{[\frac{kg \cdot m}{s}]}
L⃗ \Large \mathrm{\vec{L}}
[kg⋅m2s] \Large \mathrm{[\frac{kg \cdot m^2}{s}]}

From here down, the left side applies to both linear and rotational motion.
The right side has some additional variables that apply to rotational motion.

Kinetic Energy

Frequency

K  or  KE \Large \mathrm{K \, \, or \, \, KE}
[J] or [N⋅m] or [kg⋅m2s2] \mathrm{[J] \, or \, [N \cdot m] \, or \,} \Large \mathrm{[\frac{kg \cdot m^2}{s^2}]}
f  or  ν \Large f \, \, \mathrm{or} \, \, \nu
[Hz] or [cps] or [s−1] or [1s] \mathrm{[Hz] \, or \, [cps] \, or \, [s^{-1}] \, or \, } \Large \mathrm{[\frac{1}{s}]}

Potential Energy

Period

U  or  PE \Large \mathrm{U \, \, or \, \, PE}
[J] or [N⋅m] or [kg⋅m2s2] \mathrm{[J] \, or \, [N \cdot m] \, or \,} \Large \mathrm{[\frac{kg \cdot m^2}{s^2}]}
T \Large \mathrm{T}
[s] \Large \mathrm{[s]}

Work

Radius
(Distance from Center of Mass “CM”)

W \Large \mathrm{W}
[J] or [N⋅m] or [kg⋅m2s2] \mathrm{[J] \, or \, [N \cdot m] \, or \,} \Large \mathrm{[\frac{kg \cdot m^2}{s^2}]}
R \Large \mathrm{R}
[m] \mathrm{[m]}

Impulse

J⃗ \Large \mathrm{\vec{J}}
[N⋅s]  or   \mathrm{[N \cdot s] \, \, or \, \,} [kg⋅ms] \Large \mathrm{[\frac{kg \cdot m}{s}]}

Power

P \Large \mathrm{P}
[W]  or   \mathrm{[W] \, \, or \, \, } [Js] \Large \mathrm{[\frac{J}{s}]}   or   \mathrm{\, \, or \, \,} [kg⋅m2s3] \Large \mathrm{[\frac{kg \cdot m^2}{s^3}]}

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