= Contact-point velocity
{title2=$\mathbf v_P=\mathbf v_{\rm CM}+\boldsymbol\Omega\times\mathbf r_P$}
The instantaneous <velocity> of the material point of a <rigid body> touching another body. In the displayed formula, $\mathbf r_P$ is its position relative to the <centre of mass>, and $\boldsymbol\Omega$ is the body's <angular velocity>. The rotational term is a <cross product>. This material-point <velocity> differs from the motion of the geometrical contact location: in <rolling without slipping> on a stationary plane it vanishes even while the contact location advances. For a sphere touching a horizontal plane, with rightward centre <velocity> $v$ and anticlockwise spin $\Omega$, its tangential component is $v+a\Omega$.
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