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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 = mvG
and the angular momentum about the mass center
HG = IGω
For non-centroidal rotation, where a body rotates about a fixed point not its
mass center, the angular momentum about that fixed point is
HO = IOω
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.
GA
vA
t
A
B
Eccentric impacts occur when the mass
centers of one or both of the bodies
do not lie along the line of impact.
vB
n
GB
The coefficient of restitution can now be applied as
e = (v´Bn - v´An) / (vAn - vBn)
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.