# Apuntes fisica 3d motion

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Chapter 1

Motion in two and three dimensions

POSITION VECTOR The location of a particle relative to the origin of a coordinate system is given by a position vector [pic], which in unit vectornotation is
[pic]
Here [pic]are the vector components of position vector [pic]and x, y, and z are its scalar components (as well as the coordinates of the particle). A position vector is describedby a magnitude and one or two angles for orientation, or by its vector or scalar components.

DISPLACEMENT If a particle moves so that its position vector changes from [pic] to [pic], then theparticle's displacement [pic] is
[pic]
The displacement can also be written as
[pic]
where coordinates [pic] correspond to position vector [pic] and coordinates [pic] correspond to position vector[pic].

AVERAGE VELOCITY AND (INSTANTANEOUS) VELOCITY If a particle undergoes a displacement [pic]in time [pic], its average velocity [pic]for that time interval is
[pic]
As [pic]is shrunk to 0,[pic]reaches a limit called the velocity or instantaneous velocity[pic]:
[pic]
which can be rewritten in unit-vector notation as
[pic]
where
[pic]
The instantaneous velocity [pic]of a particle isalways directed along the tangent to the particle’s path at the particle position.

AVERAGE ACCELERATION AND (INSTANTANEOUS) ACCELERATION If a particle’s velocity changes from [pic] to [pic]in timeinterval[pic], its average acceleration [pic]during [pic] is
[pic]
As [pic]is shrunk to 0, [pic]reaches a limiting value called the acceleration or instantaneous acceleration [pic]:
[pic]
Inunit-vector notation,
[pic]
where
[pic]
The instantaneous velocity [pic]of a particle is always directed along the tangent to the particle’s path at the particle position.

INTRINSIC COMPONENTS OFACCELERATION If a particle travels along a curvilinear trajectory, it can be defined an intrinsic reference system. It has an axis tangent to the trajectory and another perpendicular or normal to the...