Answer:
[tex]\omega_f=26.43\frac{rad}{s}[/tex]
Explanation:
Arc length of the circle is the measure of the distance between two points along the circumference, is given by:
[tex]s=r\theta[/tex]
Solving for [tex]\theta[/tex] and replacing the given values:
[tex]\theta=\frac{s}{r}\\\theta=\frac{66cm}{1.7cm}\\\theta=38.82rad[/tex]
Now, we use a rotational kinematics formula in order to calculate the final angular velocity. Since the top is initially at rest [tex]\omega_0=0[/tex]:
[tex]\omega_f^2=\omega_0^2+2\alpha\theta\\\omega_f^2=2(9\frac{rad}{s^2})(38.82rad)\\\omega_f=\sqrt{698.76\frac{rad^2}{s^2}}\\\omega_f=26.43\frac{rad}{s}[/tex]