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Unformatted text preview: anets,
stars, solar systems and galaxies. It is also important on the very small scale; in particle accelerators where elementary particles are collided and
created, angular momentum is always conserved. More on Rigid Bodies
Axes and Origins
We began with a discussion of rigid bodies rotating about a fixed axis. Then we considered quantities like angular velocity, angular
acceleration, torque and angular momentum as vectors. How are the two points of view related? Torque and angular momentum vectors are
relative to an origin, where the position vector r is based at the origin. If the origin is chosen as some point on the axis then the vector relative to
the axis is just the component in the direction of the axis. The torque about some origin is the vector ”
t = r ä F.
The torque about the z axis is just the z component of this tz = t where t = r F¶ = r F sin q = r¶ F.
Similarly, the angular momentum of a particle relative to an origin ”
L = rä p
can be written relative to an axis. If the axis is the z axis then L about the axis is just the z component of L about the origin. Lz = L where L = r p¶ = r p sin q = r¶ p. Angular Momentum of a Rigid Body
As before, we view our rigid body as a collection of point masses where the perpendicular distance form the axis to mi is ri . Since all the ri
are fixed we get the momentum related...
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