The kinetic Energy of a spinning body is:

$$E_{K_{\rm total}} = \frac{1}{2}mv_{CM}^2 + I\omega^2$$

The question is: do I have to use the moment of Inertia of the center of mass? and if so, why?

thanks in advance :)


I suppose that in class you were shown how the concept of moment of inertia comes about, where the motion of a rigid body is divided into the motion of center of the mass and the motion about the center of mass.

If so, you can see how the first part in your expression for the kinetic energy ($\frac{1}{2}mv_{CM}^2$, with emphasis on the $CM$ in the subscript) is not independent from the second part, containing the moment of inertia $I$.

If you want to convince yourself, you can do a simple calculation. take a pendulum of mass $m$ on a mass-less rode of length $l$ and calculate its kinetic energy in two ways: 1) just by $\frac{1}{2}mv^2$ and 2) by considering it as a rigid body rotating about the point where it is fixed to the ceiling.

  • $\begingroup$ Thank you for your helpful answer. it helped me see the connection between the parts of the equation! It makes sense to me now :) $\endgroup$ – Aviv Levi Jan 24 at 13:54

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