## Essential University Physics: Volume 1 (3rd Edition)

a) $\frac{2ML^2}{3}$ b) $\frac{2ML^2}{3}$ c) $\frac{4ML^2}{3}$
a) The rotational inertia depends on whether the rod is perpendicular or parallel to the axis of rotation. Thus, using the equations for moment of inertia, we find: $I=(\frac{1}{12}+\frac{1}{4})mL^2 =\frac{ML^2}{3}$ Since there are two of each rod, the total inertia is: $\frac{2ML^2}{3}$. b) While this is oriented differently, the mass of the uniform square is the same distance away on average, so the inertia is the same. Thus: $I= \frac{2ML^2}{3}$. c) We find the inertia of all of the four rods: $I=4(\frac{1}{12}+\frac{1}{4})mL^2 =\frac{4ML^2}{3}$