Answer
The angular velocity at the end of the third minute is $0.4~\omega$
Work Step by Step
We can find an expression for the angular acceleration:
$\alpha = \frac{\Delta \omega}{\Delta t} = \frac{-0.20~\omega}{1~min}$
We can find the angular velocity after 3.0 minutes:
$\omega_f = \omega_0+\alpha~t$
$\omega_f = \omega+(\frac{-0.20~\omega}{1~min})(3.0~min)$
$\omega_f = \omega+(-0.60~\omega)$
$\omega_f = 0.4~\omega$
The angular velocity at the end of the third minute is $0.4~\omega$
