The final angular velocity is 8.6 rad/s
Explanation:
To solve this problem, we can use the equivalent of the suvat equations for the angular motion. In particular, we can use the following equation:
[tex]\omega_f = \omega_i + \alpha t[/tex]
where:
[tex]\omega_f[/tex] is the final angular speed
[tex]\omega_i[/tex] is the initial angular speed
[tex]\alpha[/tex] is the angular acceleration
t is the time
For the propeller in this problem, we have:
[tex]\omega_i = 3.8 m/s[/tex] is the initial angular speed
[tex]\alpha=1.6 rad/s^2[/tex] is the angular acceleration
Substituting t = 3.0 s in the equation, we find the final angular velocity:
[tex]\omega_f = (3.8)+(1.6)(3.0)=8.6 rad/s[/tex]
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