Unit 19
MAIN POINTS
Angular Momentum Definition
The angular momentum L
&
of a
point particle about some axis is
defined to be the cross product of
r
&
, the vector from the axis to the
particle, with p
&
, the momentum
vector of the particle.
The angular momentum of a
system of particles about a fixed
axis is equal to the vector sum of
the individual angular momenta.
The angular momentum for a
system of particles rotating about a
common axis with a fixed angular
velocity is equal to the product of
the moment of inertia of the system
about the axis and the angular
velocity vector.
Rotational Equation of Motion
We used Newton’s second law to obtain the
rotational equation of motion, namely, that the
sum of the external torques acting on a system is
equal to the time rate of change of the angular
momentum of the system.
Consequently, if the sum of the external torques on a system is zero, the angular
momentum of the system is conserved.
d
t
Ld Total
ExternalNet
&
&=
,
τ
prL &&
&
×≡ ¦
=iTotal LL
&&
ω
&
&
system
IL =