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**Hint**Since the wheel is going to stop, hence final angular acceleration = 0. Now use the equation ${\omega _f} = {\omega _i} + \alpha t$ to get the value of α. Also convert units of ω to rad/sec.

**Complete step-by-step answer:**

Given that,

The Initial angular velocity of the wheel, (\[{\omega _i}\] )= 33 rev/min

The Final angular velocity of the wheel, (\[{\omega _f}\]) = 0

Time taken by wheel to stop (t) = 20 second = 20s .

We know that,

The initial angular velocity in rad/s (\[{\omega _i}\]) is given by =

$

\Rightarrow 33 \times \dfrac{{2\pi }}{{60}} \\

\Rightarrow 1.1\pi \,{\text{rad/s}} \\

$ ($\dfrac{{2\pi }}{{60}}$ is the conversion factor from revolution/minute to radian/sec.)

The angular retardation can be calculated by using the formula,

(Since retardation is mentioned, hence we have to take the negative value of alpha and not positive value.) .

\[

{\omega _f} = {\omega _i} - \alpha t \\

\Rightarrow 0 = 1.1\pi - \alpha \times 20 \\

\Rightarrow \alpha = \dfrac{{1.1\pi }}{{20}} = \dfrac{{11\pi }}{{200}} \\

\] (Putting the values given in the question, we have the following.)

**Hence, the angular retardation of the wheel will be \[\dfrac{{11\pi }}{{200}}\] rad/${s^2}$.**

**Note**All the three equations of motion can be used in circular motion just by changing the few notations like “a” (acceleration) with \[\alpha \](angular acceleration), S (displacement) with θ (angular displacement), velocity (v) with omega (ω). But time remains the same.

E.g.

$v = u + at$ is similar to ${\omega _f} = {\omega _i} + \alpha t$ .

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