For the equations for I given in parts (a) and (b) of Table 9.2 to be valid, must the rod have a circular cross section? Is there any restriction on the size of the cross section for these equations to apply? Explain.

Solution 15DQ Introduction We have to discuss if the formula given for the moment of inertia of rod in the section (a) and (b) of table 9.2. Step 1 In the derivation of the formula, the thickness was considered to be infinitesimally small. So the shape of the cross section was neglected. Hence, it does not matter whether the cross section is a circle or rectangle, the formula will hold true as long as the thickness is very small compared to its length. So the cross section need not to be a circle for this formula to be valid.