Answer
$-19,800~J~~$ of work must be done to stop the wheel.
Work Step by Step
We can express the angular speed in units of $rad/s$:
$\omega = (280~rev/min)(\frac{2\pi~rad}{1~rev})(\frac{1~min}{60~s}) = 29.32~rad/s$
We can find the initial rotational kinetic energy of the wheel:
$K = \frac{1}{2}I~\omega^2$
$K = \frac{1}{2}MR^2~\omega^2$
$K = (\frac{1}{2})(32.0~kg)(1.20~m)^2~(29.32~rad/s)^2$
$K = 19,800~J$
$-19,800~J~~$ of work must be done to stop the wheel.
