 Rigid-body collision

A rigid-body collision changes both translation and rotation through a short contact impulse. For a freely moving body of mass $M$, an impulse $\mathbf{J}$ applied at displacement ${\mathbf{r}}_c$ from its center of mass giveswhere $\mathbf{L}$ is angular momentum about the center of mass. An off-centre hit can therefore create spin even when the incoming body had none.

The relevant collision velocity is the relative contact-point velocity, including rotational motion. A normal restitution law and a tangential contact or friction law are needed to determine the impulse; conservation of total momentum alone does not specify the outcome. A ball struck through its centre and the same ball struck off-centre illustrate this distinction. The rigid approximation describes the before-and-after motion while replacing the short deformation process by an impact law.