Moments Between Impacting Rigid Bodies

Abstract

It appears that all current literature in mechanics omits the effect of the moment developed between colliding rigid bodies. In many practical applications in design work, a significant moment can exist during impact and the impulse of the moment must be included in the equations for the change of angular momentum of each body. The general equations of impulse and momentum are presented for two rigid bodies colliding in planar motion. These reduce to six linear equations in the six unknown final velocities. The effect of the moment impulse on the angular velocities is taken into account through the use of a moment coefficient of restitution. This coefficient can take on realistic values between minus and plus one. Several examples are worked. An expression for the moment coefficient is derived for a vertically falling block which rebounds with a non zero angular velocity. This angular velocity is related to nonuniformities in the surface impacted by the block.