Answer:
1300 rad ([tex]74522^{\circ}[/tex])
Explanation:
The angular speed of an object is the rate of change of angular position.
It is given by:
[tex]\omega=\frac{\theta}{t}[/tex]
where
[tex]\omega[/tex] is the angular speed
[tex]\theta[/tex] is the angular displacement of the object
t is the time elapsed
For the propeller rotating in this problem, we have
[tex]\omega=260 rad/s[/tex] is the angular speed
t = 5.0 s is the time elapsed
Therefore, the angular displacement is:
[tex]\theta=\omega t=(260)(5.0)=1300 rad[/tex]
And since [tex]2\pi rad = 360^{\circ}[/tex], the angle in degrees is
[tex]\theta=\frac{1300}{2\pi}(360)=74522^{\circ}[/tex]
