To solve this problem it is necessary to apply the concepts related to rotational kinetic energy, the definition of the moment of inertia for a sphere and the obtaining of the radius through the circumference. Mathematically kinetic energy can be given as:
[tex]KE= I\omega^2[/tex]
Where,
I = Moment of inertia
[tex]\omega =[/tex] Angular velocity
According to the information given we have that the radius is
[tex]\Phi= 2\pi r[/tex]
[tex]0.749m = 2\pi r[/tex]
[tex]r = 0.1192m[/tex]
With the radius obtained we can calculate the moment of inertia which is
[tex]I = \frac{2}{3}mr^2[/tex]
[tex]I = \frac{2}{3}(0.624)(0.1192)^2[/tex]
[tex]I = 5.91*10^{-3} kg \cdot m^2[/tex]
Finally, from the energy equation and rearranging the expression to obtain the angular velocity we have to
[tex]\omega = \sqrt{\frac{2KE}{I}}[/tex]
[tex]\omega = \sqrt{\frac{2(1.99)}{5.91*10^{-3}}}[/tex]
[tex]\omega = 25.95rad/s[/tex]
Therefore the angular speed will the ball rotate is 25.95rad/s
