= Adhesive collision of two equal discs
Two uniform discs of <mass> m and radius a stick at first edge contact. One initially translates at <speed> v and the other rests, with neither initially spinning. If the incoming <velocity> makes angle $\theta$ to the line of centres, the composite axial <moment of inertia> about its <centre of mass> is $3ma^2$. Conserved angular-momentum magnitude is $mav|\sin\theta|$, so the <angular velocity> magnitude is $v|\sin\theta|/(3a)$. The centre-of-mass <speed> is v/2. Splitting <kinetic energy> into translation and rotation gives $K_f=mv^2(1/4+\sin^2\theta/6)$. The difference from $mv^2/2$ is dissipated internally; it cannot be removed from angular-momentum conservation.
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