initial angular speed of the wheel is given by
[tex]w_0 = 300 rev/min[/tex]
[tex]w_0 = 2\pi * \frac{300}{60}[/tex]
[tex]w_0 = 31.4 rad/s[/tex]
angular displacement of wheel till it stops
[tex]\theta = 2 \pi N = 2\pi * 88[/tex]
[tex]\theta = 552.92 rad[/tex]
now by the kinematics equations we will have
[tex]w^2 - w_0^2 = 2\alpha \theta[/tex]
[tex] 0 - 31.4^2 = 2*\alpha * 552.92[/tex]
[tex]\alpha = -0.89 rad/s^2[/tex]
