Take the tour ×  Usually, the angular frequency $\omega$ is
given in $\mathrm{1/s}$. I find it more consistent to give it in
$\mathrm{rad/s}$. For the angular momentum $L$ is then given in
$\mathrm{rad \cdot kg \cdot m^2 / s}$.  However, the relation
for torque $\tau$ says: $$ \tau \cdot t = L$$  So the torque
should not be measured in $\mathrm{N \cdot m}$ but $\mathrm{rad
\cdot N \cdot m}$. Would that then be completely consistent?
share|improve this question More on radians:
physics.stackexchange.com/q/33542/2451 –  Qmechanic Sep 10 '12
at 19:34 add comment  2 Answers  up vote 4 down vote accepted
OP wrote(v1):  So the torque should not be measured in N⋅m but
rad⋅N⋅m. Would that then be completely consistent?  No, that
would not be consistent with the elementary definition of torque
$\vec{\tau}=\vec{r} \times \vec{F}$ as a cross-product between a
position vector $\vec{r}$ and a force vector $\vec{F}$.  An
angle in radians is the ratio between the length of a circle arc
and its radius, and is therefore dim