Answer
The kinetic energy of the shell is 8.88 J.
Work Step by Step
We can find the angular speed of the sphere.
$\omega^2 = 2 ~\theta ~\alpha$
$\omega = \sqrt{2 ~\theta ~\alpha}$
$\omega = \sqrt{(2)(6.00~rev)(2\pi~rad/rev)(0.890~rad/s^2)}$
$\omega = 8.192~rad/s$
We can find the kinetic energy of the shell.
$KE = \frac{1}{2}I\omega^2$
$KE = \frac{1}{2}(\frac{2}{3}mr^2)\omega^2$
$KE = \frac{1}{3}(mr^2)\omega^2$
$KE = \frac{1}{3}(8.20~kg)(0.220~m)^2(8.192~rad/s)^2$
$KE = 8.88~J$
The kinetic energy of the shell is 8.88 J.
