# Where does the angular momentum of relativistic objects go? [closed]

Suppose you are floating in outer space and there is a massive sphere of mass $$1 \text{kg}$$ next to you and radius $$1$$ meter and an angular velocity of $$1$$ revolutions a second. Using the formula for the moment of inertia of a solid sphere $$I = \frac{2}{5}MR^2$$ and the formula for angular momentum $$L = I\omega$$ we conclude that the sphere has an angular momentum of $$\frac{2}{5}$$ $$\frac{\text{kg} \cdot \text{m}^2 }{\text{s}}$$

Now a mysterious force suddenly sends the sphere flying away from you at $$0.99c$$ according to your frame of reference (maybe a bomb goes off on one side of the sphere). Naturally now that the sphere is moving very fast you proceed to calculate the rate of rotation of the sphere and conclude that it is rotating at $$\sqrt{1 - \frac{(0.99c)^2}{c^2} }$$ revolutions per second or about $$0.14$$ revolutions per second.

You thus conclude the total angular momentum in this universe is now $$\frac{2}{5} * 0.14$$

Of course this feels a bit strange considering that angular momentum is normally a conserved quantity so where has the angular momentum GONE in this system?

The "bomb" going off is a suspicious culprit here but that could easily be replaced with say a bunch of lasers pushing on the sphere and again it would appear that lasers can just make angular momentum disappear in SR.

Perhaps a more sophisticated way to ask this question is, if not angular momentum itself, what is the correct generalization of angular momentum that is preserved in special relativity?

• You are mixing non-relativistic formulæ with relativistic formulæ, so obviously there will be something wrong. You would have to use relativistic formulæ consistently and properly to get an agreeable answer. In fact, because of how you have randomly inserted this bomb, you can engineer it to give excess angular momentum in NR in any direction you wish. Your question is just your own confusion. In practice, it is far easier to simply start with a parametrisation respecting linear and angular momentum conservation. Commented Jul 2 at 1:35
• en.wikipedia.org/wiki/Relativistic_angular_momentum Commented Jul 2 at 12:10