# Angular and linear momentum conservaion in collision

I have a problem that is seriously challenging both my intuition in what might happen and my ability of expressing the maths.

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Imagine you have a sphere of radius $R$ with CoM speed $\mathbf{v_0}$ and rotating about its axis at $\mathbf{\omega_0}$. In space. It collides with another identical sphere, at rest at not rotating. What happens to the final linear velocities $\mathbf{v_1}$, $\mathbf{v_2}$, and angular velocities $\mathbf{\omega_1}$ and $\mathbf{\omega_2}$? Both sphere have rough surfaces so there is some exchange of angular velocity.

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I've tried normal angular momentum, linear momentum and total (linear + rotational) energy conservation, but I get 4 variables ($\mathbf{v_1}, \mathbf{v_2}, \mathbf{\omega_1}, \mathbf{\omega_2}$) with only 3 equations.

Can I decouple linear and rotational motion since they should not be talking to one another?

What should I take as a point where to calculate angular momenta from?

• Given that "both spheres have rough surface", you can toss conservation of mechanical energy out the window. Some of the initial mechanical energy will be converted to thermal energy. Also, your equations for conservation of linear and angular momentum are three equations each. Finally, don't forget about the angular momentum due to translation. – David Hammen Mar 6 '17 at 0:46