Answer:
[tex]\omega '=-13.5rad/s[/tex]
Explanation:
From the question we are told that:
Time [tex]t=4sec[/tex]
Angular displacement [tex]\theta= 161 rad[/tex]
Final Angular velocity [tex]\omega = 100 rad / s[/tex]
Let
Angular acceleration [tex]\alpha[/tex]
Generally the equation for Initial Angular velocity [tex]\omega '[/tex] is mathematically given by
[tex]-\omega '^2=2 \alpha \theta -\omega^2[/tex]
[tex]\omega '^2= \alpha 328 +11236[/tex]
Also,Initial Angular velocity [tex]\omega '[/tex] is mathematically given by
[tex]\omega '=\omega - \alpha t[/tex]
Therefore substitution
[tex]-\omega '^2=2 \alpha \theta -\omega^2[/tex]
[tex]\omega '=\omega - \alpha t[/tex]
[tex](\omega - \alpha t)^2=2 \alpha \theta -\omega[/tex]
[tex]-16\alpha^2+848\alpha+11236= \alpha 328 -11236[/tex]
[tex]16\alpha^2-520\alpha=0[/tex]
[tex]\alpha=29.875rads/s^2[/tex]
Substitution in the 2nd equation for Initial Angular velocity [tex]\omega '[/tex]
[tex]\omega '=106-(29.875rads/s^2*4)[/tex]
[tex]\omega '=-13.5rad/s[/tex]
