## College Physics (4th Edition)

$\tau = I~\alpha$ 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.
$\tau = I~\alpha$ $I$ 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.