# Apuntes fisica 3d motion

Páginas: 3 (669 palabras) Publicado: 3 de mayo de 2010
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...

Regístrate para leer el documento completo.