# Problem: Calculate the moment of inertia and the rotational kinetic energy for the following objects spinning about a central axis (in units of Joules): a. a solid sphere with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec. b. a thin spherical shell with a mass of 200 grams and a radius of cm rotating with an 5.0 angular speed of 2.5 rad/sec.

###### FREE Expert Solution

Rotational kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{I}}{{\mathbf{\omega }}}^{{\mathbf{2}}}}$

a.

For a solid sphere, the moment of inertia about its central axis is given by:

I = (2/5)MR2

###### Problem Details

Calculate the moment of inertia and the rotational kinetic energy for the following objects spinning about a central axis (in units of Joules):

a. a solid sphere with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec.

b. a thin spherical shell with a mass of 200 grams and a radius of cm rotating with an 5.0 angular speed of 2.5 rad/sec.