Problem 10.15

10.15. a)

We know that in general
$I = \sum_{j} m_{j} r_{j}^{2}$
so in this case, j ranges from 1 to 4, and
r₁=r₂=r₃=r₄
$r = \sqrt{(3m)^{2}+(2m)^{2}} ~=~ \sqrt{13} m$
and therefore,
$I = (\sqrt{13} m)^{2} (3+2+2+4) kg$$I = 143 kg\cdot m^{2}$

In part b) we want the kinetic energy of the system. This is given by
$K = \frac{1}{2} I \omega^{2}$
$K = \frac{1}{2} (143 kg \cdot m^{2})(6 rad/s)^{2}$
or $K = 2.57 \times 10^{3} J$