Answer
At $t = 0$, the rotational kinetic energy is $~~0.40~J$
Work Step by Step
We can find an expression for the rotational kinetic energy at $t = 4.0~s$:
$K_4 = \frac{1}{2}I~\omega_4^2$
$K_4 = \frac{1}{2}I~(4.0~rad/s)^2$
$K_4 = (8~I)~~J$
We can find the rotational kinetic energy at $t = 0$:
$K_0 = \frac{1}{2}I~\omega_0^2$
$K_0 = \frac{1}{2}I~(-2.0~rad/s)^2$
$K_0 = (2~I)~J$
$K_0 = \frac{K_4}{4}$
$K_0 = \frac{1.6~J}{4}$
$K_0 = 0.40~J$
At $t = 0$, the rotational kinetic energy is $~~0.40~J$
