Answer:
930.21J
Explanation:
The kinetic energy of a solid body that is rotating, is given by:
[tex]E_k=\frac{1}{2}I\omega^2[/tex]
where I is the moment of inertia and w is the angular velocity.
The moment of inertia for a spherical shell is:
[tex]I=\frac{2}{3}MR^2[/tex]
where M is the mass and R is the radius of the sphere. By replacing we have
[tex]I=\frac{2}{3}(8.05kg)(0.215m)^2=0.55\ kgm^2[/tex]
To calculate w we have to use the equation
[tex]\omega^2=\omega_0^2+2\alpha \theta\\\\\omega=\sqrt{2(0.895rad/s^2)(5.25rev*\frac{360\°}{1\ rev})}=58.16\frac{rad}{s}[/tex]
where we have taken w0=0 rad/s.
Finally, by replacing I and w we obtain:
[tex]E_k=\frac{1}{2}I\omega^2 =\frac{1}{2}(0.55\ kgm^2)(58.16\frac{rad}{s})^2=930.21J[/tex]
HOPE THIS HELPS!
