Angular Momentum
The final concept we develop for rotational motion is that of angular momentum. We will give
the same treatment to angular momentum that we did to linear momentum: first we develop the
concept for a single particle, then generalize for a system of particles.
Angular Momentum for a Single Particle
Consider a single particle of mass m travelling with a velocity
v
a radius
r
from an axis, as shown
below.
Figure %: A single particle moving with respect to an axis, O
The angular momentum of the single particle, then, is defined as:
l
=
rmv
sin
θ
Notice that this equation is equivalent to
l
=
rp
sin
θ
, where
p
is the linear momentum of the
particle: a particle does not need to move in a circular path to possess angular momentum.
However, when calculating angular momentum, only the component of the velocity moving
tangentially to the axis of rotation is considered (explaining the presence of sin
θ
in the equation).
Another important aspect of this equation is that the angular momentum is measured relative to
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 Fall '10
 DavidJudd
 Physics, Angular Momentum, Momentum

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