Answer:
K = 9.41 J
Explanation:
The kinetic energy of a spherical shell is given as:
[tex]k = \frac{1}{2} I \omega^2[/tex]
where I = moment of inertia and
ω = angular velocity
Let us find I:
For a hollow sphere:
[tex]I = \frac{2}{3} MR^2[/tex]
where M = mass = 8.35 kg
R = radius = 0.225 m
[tex]=> I = \frac{2}{3} * 8.35 * 0.225^2 = 0.282 kgm^2[/tex]
Let us find ω:
Since angular acceleration is constant:
[tex]\omega^2 = \omega_0^2 + 2\alpha(\theta - \theta_0)\\\\\omega_0 = 0\\\\=>\omega^2 = 2\alpha(\theta - \theta_0)\\\\\theta - \theta_0 = 6 * (2 * \pi) = 37.70 rad\\\\\omega^2 = 2 * 0.885 * 37.70 = 66.729[/tex]
Therefore, its kinetic energy is:
[tex]K = \frac{1}{2} * 0.282 * 66.729\\\\K = 9.41 J[/tex]
