The initial angular speed of the wheel is (keeping in mind that [tex]1 rev=2 \pi rad[/tex]):
[tex]\omega _i=35 rev/s \cdot ( 2 \pi \frac{rad}{rev})=219.8 rad/s [/tex]
The final angular speed instead is:
[tex]\omega _f=15 rev/s \cdot ( 2 \pi \frac{rad}{rev})=94.2 rad/s [/tex]
Therefore we can find the value of the angular acceleration:
[tex]\alpha = \frac{\omega _f-\omega _i}{t}= \frac{94.2 rad/s-219.8rad/s}{3.0 s}=-41.87 rad/s^2 [/tex]
and the negative sign is due to the fact the wheel is decelerating.
