EGR 280 Mechanics 18 – Impulse and Momentum of Rigid Bodies

Kinetics of rigid bodies in plane motion – Impulse and Momentum We have seen that, for a particle or a system of particles, (momentum) 1 + (external impulse) 1→2 = (momentum) 2 For rigid bodies, the total momentum is in two parts: the linear momentum of the mass center L = mv G and the angular momentum about the mass center H G = I G ω For non-centroidal rotation, where a body rotates about a fixed point not its mass center, the angular momentum about that fixed point is H O = I O ω

Conservation of Angular Momentum When no external forces act on a system of rigid bodies, both the linear and angular momenta of the bodies are conserved. Often, the linear momentum of a rigid body is not conserved, but the angular momentum about some point may be conserved. Such a point would be on the line of action of the resultant external force.

Eccentric Impact We have looked at direct impacts, where the mass centers of the bodies lie on the line on impact, n. Eccentric impacts occur when the mass centers of one or both of the bodies do not lie along the line of impact. A B GAGA GBGB n t vAvA vBvB

The coefficient of restitution can now be applied as e = (v´ Bn - v´ An ) / (v An - v Bn ) where ()´ is a velocity after impact and () n is a velocity component along the line of impact. This equation, along with conservation of momentum, is used to find the velocities of points A and B after impact. This relationship also applies if one or both of the bodies are constrained to rotate about fixed points.