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## Homework Statement

Hi all! I have a very simple problem, which seems to get two different answers depending on whether you use conservation of angular momentum, or energy. Both quantities seem to be conserved:

Initially we have a disk of radius a spinning about its center of mass at known angular velocity ω. Suddenly a random point along the disks diameter becomes fixed in place and the disk begins spinning about that point with angular velocity Ω. Find the final angular velocity Ω.

## Homework Equations

Using conservation of angular momentum:

##L_i=I_{CM}*\omega=\frac{1}{2}ma^2*\omega##

##L_f=I_{edge}*\Omega=(I_{CM}+ma^2)*\Omega=\frac{3}{2}ma^2*\Omega##

⇒##L_i=L_f##

⇒##\Omega=\frac{1}{3}*\omega##

Using Conservation of energy:

##E_i=\frac{1}{2}I_{CM}\omega^2=\frac{1}{4}ma^2\omega^2##

##E_f=\frac{1}{2}I_{edge}\Omega^2=\frac{3}{4}ma^2\Omega^2##

⇒##E_i=E_f##

⇒##\Omega=\frac{1}{\sqrt{3}}*\omega##

## The Attempt at a Solution

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As you can see, both methods give similar results, but not the same. Why would this be? If there some reason why Energy or Angular momentum would not be conserved? Is it something to do with the fact that angular momentum is only conserved about the center of mass, which it is no longer spinning about in the final scenario?

Thank you in advance!