Answer:
54.4747649021
38.2003395586 rad/s
Explanation:
Acceleration
[tex]v=u+at\\\Rightarrow a=\dfrac{v-u}{t}\\\Rightarrow a=\dfrac{22.5-0}{8.96}\\\Rightarrow a=2.51116071429\ m/s^2[/tex]
Distance covered
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0\times t+\dfrac{1}{2}\times 2.51116071429\times 8.96^2\\\Rightarrow s=100.8\ m[/tex]
Number of revolutions
[tex]n=\dfrac{s}{\pi d}\\\Rightarrow n=\dfrac{100.8}{\pi 0.589}\\\Rightarrow n=54.4747649021[/tex]
Number of revolutions is 54.4747649021
Angular speed is given by
[tex]\omega=\dfrac{v}{r}\\\Rightarrow \omega=\dfrac{22.5}{0.589}\\\Rightarrow \omega=38.2003395586\ rad/s[/tex]
The final angular speed is 38.2003395586 rad/s
