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According to multiple sources the SI units for angular momentum are kg * m$^2$ / sec

I am confused about the derivation for this. Here is what I have done:

$$L = I \cdot \omega \\ = m \cdot r^2 \cdot r \cdot v(translational) \\ = kg \cdot m^3 \cdot m/s \\ = (kg \cdot m^4)/s$$

What are my doing wrong here

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$\omega$ is $\left[ T^{-1}\right]$. – Ali Apr 13 '14 at 22:09

Your mistake is your definition of the angular velocity $$ \omega=rv \tag{not correct} $$ is incorrect. We know that $\omega$ has units of $1/s$, but your assertion gives it units of $m^2/s$. The correct definition is $$ \omega=\frac vr \tag{correct} $$ which gives the correct units. Using this: $$ \left[L\right] = [m]\left[r^2\right]\cdot\left[v\cdot r^{-1}\right]=kg\cdot m^2\cdot\frac ms\cdot\frac1m=kg\,m^2\,s^{-1} $$

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