Question

Find the kinetic energy of the uniform circular cone of height h, base radius R, and mass M. Rotating with the angular velocity Ω around an axis which goes through the ~ center of mass.

Answer 1

`E_k = M\Omega^2\left((3)/(40)R^2 + (3)/(160)h^2\right)`

Step-by-step explanation:

The (rotational) kinetic energy of the right uniform circular cone is as the following:

`E_k = I\omega^2/2`

where
`\omega = \Omega` is the angular speed, I is the moments of inertia about the axis of rotation, which goes through the center of mass:

`I = M\left((3)/(20)R^2 + (3)/(80)h^2\right)`

Therefore:

`E_k = M\Omega^2\left((3)/(40)R^2 + (3)/(160)h^2\right)`