1
$\begingroup$

I have an ellipsoid that changes into a sphere. I want to calculate $\delta p / p_{initial}$ in terms of the eccentricity $e$.

I'm given that the moment of inertia of an ellipsoid is approximately $2/5 Ma^2$. I know that the volume of an ellipsoid is $\frac{4 \pi}{3}a^2b$, and eccentricity is $e = c / a$, where $a$ is the longest semimajor axis of the ellipsoid, and $b$ is the shortest. $c$ is the distance from the ellipsoid's center to the focus. I know that the final ellipticity of the sphere is zero (since c=0).

Given this information, I am trying to calculate the change in period over the initial period in terms of $e$. How would I go about doing this? Thanks.

Improve this question
$\endgroup$
5
  • 1
    $\begingroup$ The period of what motion? $\endgroup$
    – G. Smith
    Commented Apr 9, 2019 at 0:05
  • $\begingroup$ The rotation of the object. $\endgroup$
    – user203234
    Commented Apr 9, 2019 at 0:43
  • $\begingroup$ Around what axis? $\endgroup$
    – G. Smith
    Commented Apr 9, 2019 at 3:22
  • 1
    $\begingroup$ An general ellipsoid has three different semi-major axis lengths. You seem to be talking about a spheroid. $\endgroup$
    – G. Smith
    Commented Apr 9, 2019 at 5:26
  • $\begingroup$ Given the equation for the moment of inertia being only in a, rotation would be about the short axis of an oblate spheroid. $\endgroup$
    – Paul Childs
    Commented Apr 9, 2019 at 5:56

1 Answer 1

Reset to default
1
$\begingroup$

The angular momentum, given as $L = I \omega$, is a conserved quantity. Given more context, it might not be the case, but if so then you are stuck. Therefore:

$$\frac{d\tau}{\tau} = \frac{d(Ma^2)}{Ma^2}$$

Now you say the spheroid is changing. In what way is it changing? Is M constant? Is the volume constant? Or is it that a is constant?

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.