1

I can find formulas for the kinetic energy of a globe (ball) in motion but not for just rotating. Anyone has the formula to calculate the kinetic energy of a rotating globe?

Johnny
  • 11

1 Answers1

1

The total kinetic energy of a body is sum of translational and rotational kinetic energies

$$K = \frac{1}{2} m v^2 + \frac{1}{2} I \omega^2$$

where $v$ is translational speed of center of mass, $\omega$ is rotational velocity, and $I$ is moment of inertia about axis of rotation. Moment of inertia of a homogeneous solid sphere is $I = \frac{2}{5} m r^2$ where $r$ is sphere radius. Note that the Earth is not homogeneous solid sphere but could be approximated as one within some margin of error.

Marko Gulin
  • 5,210
  • 1
    Great answer. Just to clarify: "translational" is the movement from the original position (like a bullet shot out of a gun). Correct? – Johnny Mar 20 '22 at 15:27
  • @Johnny Correct, translational motion causes change of position of the center of mass in space. – Marko Gulin Mar 20 '22 at 15:33
  • Many thanks for your insight! – Johnny Mar 20 '22 at 15:36
  • @Johnny I am glad it helped. – Marko Gulin Mar 20 '22 at 15:37
  • 1
    Note that the formula for moment of inertia holds only for a homogenous sphere. If the sphere is not homogenous (such as Earth), the formula serves only as an approximation. In the limit of a point, $I=0$, and in the limit of a spherical shell, $I=mr^2$. – User123 Mar 20 '22 at 18:20
  • @User123 In earlier version of the post I had "ideal solid sphere". I agree that "homogeneous" is much better word than "ideal" in this context. Thanks for the suggestion! – Marko Gulin Mar 20 '22 at 20:08