Answer
$\tau = I~\alpha$
Both sides of the equation have units of $N \cdot m$. Therefore, the units of the rotational form of Newton's second law are consistent.
Work Step by Step
$\tau = I~\alpha$
$I$ is the rotational inertia in units of $kg~m^2$
$\alpha$ is the angular acceleration in units of $rad/s^2$
We can verify the units of $I~\alpha$:
$(kg~m^2)~(rad/s^2) = \frac{kg~m^2}{s^2} = \frac{kg~m}{s^2} \cdot m = N \cdot m$
A torque is calculated by $\tau = r\times F$, where $r$ has units of $m$ and $F$ has units of $N$. Then $\tau$ also has units of $N \cdot m$
Since both sides of the equation have units of $N \cdot m$, the units of the rotational form of Newton's second law are consistent.
