Answer
$K = 0.94~J$
Work Step by Step
We can find the rotational inertia:
$I = \frac{1}{3}ML^2$
$I = \frac{1}{3}(0.42~kg)(0.75~m)^2$
$I = 0.118~kg~m^2$
We can find the rotational kinetic energy at the lowest position:
$K = \frac{1}{2}I~\omega^2$
$K = (\frac{1}{2})(0.118~kg~m^2)(4.0~rad/s)^2$
$K = 0.94~J$
