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I derived the following formula for change in angular velocity after a collision using conservation of angular momentum.

$$I_1 ω_i+I_2 ω_2i=I_1 ω_f+I_2 ω_2f$$ $$I_1 ω_i-I_1 ω_f=I_2 ω_2f-I_2 ω_2i$$ $$I_1 (ω_i-ω_f)=I_2 (ω_2f-ω_2i)$$ $$Δω_1=(-Δω_2 I_2)/I_1$$

And I noticed that the only thing that matters is the change in velocity of the other object, not the initial velocity. That doesn't make much sense to me though, even if the change in the other object is the same, shouldn't an object with more initial velocity lose less velocity?

user305283
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  • Does this help? https://physics.stackexchange.com/a/529743/392 – John Alexiou Sep 13 '21 at 00:47
  • The above might be valid if the axis of rotation remains fixed and the mass moment of inertia is constant. But in general, this is 3D problem, and you are treating vectors as scalars. Angular momentum is $$ \overline{L} = \mathrm{I}, \overline{\omega}$$ where ${\rm I}$ is a 3x3 matrix. – John Alexiou Sep 17 '21 at 21:48

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