Chapter 1, Problem 2PP

(Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a cylinder, this moment of inertia is given by this formula:

$\begin{array}{l}{\text{J = mr}}^{\text{2}}\text{ / 2 + m}\left({\text{l}}^{\text{2}}{\text{ + 3r}}^{\text{2}}\right)\text{ / 12}\hfill \\ \text{m is the cylinder’s mass }\left(\text{kg}\right)\text{.}\hfill \\ \text{l is the cylinder’s length }\left(\text{m}\right)\text{.}\hfill \\ \text{r is the cylinder’s radius }\left(\text{m}\right)\text{.}\hfill \end{array}$

Using this formula, determine the units for the cylinder’s polar moment of inertia.