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    $\begingroup$ 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. $\endgroup$
    – naturallyInconsistent
    Commented Jul 2 at 1:35
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    $\begingroup$ en.wikipedia.org/wiki/Relativistic_angular_momentum $\endgroup$
    – alanf
    Commented Jul 2 at 12:10