Impulse-driven slipping-to-rolling transition of a sphere
= Impulse-driven slipping-to-rolling transition of a sphere
For a uniform sphere struck horizontally with <impulse> $J$ at height $d$ above its centre, $u_0=J/M$ and clockwise spin $\Omega_0=5Jd/(2Ma^2)$. <friction> brings the contact slip $u-a\Omega$ to zero. The final rolling <speed> is $u_f=5J(1+d/a)/(7M)$, independent of a positive constant <friction> coefficient; <friction> can accelerate an initially overspinning <centre of mass>.