Initial angular frequency is given as
[tex]f = 10,000 rpm[/tex]
now convert it into rounds per seconds
[tex]f = 10000\times \frac{1}{60} = 166.67 Hz[/tex]
now initial angular speed is given as
[tex]\omega = 2 \pi f[/tex]
[tex]\omega = 2\pi (166.67)[/tex]
[tex]\omega = 1047.2 rad/s[/tex]
now finally it comes to rest in t = 17 s
now we can use kinematics equation to find the angular acceleration
[tex]\omega_f - \omega_i = \alpha t[/tex]
[tex]0 - 1047.2 = \alpha (17)[/tex]
[tex]\alpha = - 61.6 rad/s^2[/tex]
so angular acceleration will be 61.6 rad/s^2
