= Floor-impulse dependence of a rolling-cylinder collision
A smooth central <collision> leaves a cylinder's <angular velocity> unchanged if the floor supplies negligible tangential <impulse>. Imposing <rolling without slipping> during the impact instead requires a floor <impulse> and changes the cylinder's effective translational <mass> to $m+I/r^2$. Consequently a pre-impact rolling condition alone does not determine the outgoing <velocities>: the impulsive contact law must also be specified. For a uniform solid cylinder striking a stationary <point mass> $2m$ in an <elastic collision>, the target acquires $2u/3$ with negligible floor <impulse>, and $6u/7$ with an enforced rolling constraint, where $u$ is the incoming centre <speed>.
Back to article page
