Modified 2018-06-24 by Andrea Censi
Required Reading: The following assumes a working familiarity with 2D and 3D Cartesian coordinate systems. If you are not familiar with Cartesian coordinate systems, please read the chapter on coordinate systems (unknown ref preliminaries/coordinate_systems)
.Modified 2018-06-22 by Andrea Censi
Does Earth move around the sun or does the sun move around Earth? It turns out that this is an ill-posed question until we specify a frame of reference for measurement. For us, observers on Earth, it appears that the sun is moving. But for an observer on the moon, both Earth and the sun are moving. In general, motions are relative and we need a reference when measuring motion.
Modified 2018-06-22 by Andrea Censi
A reference frame, or just frame, is an abstract coordinate system and the set of physical reference points that uniquely specify the coordinate system (location of the origin and orientation). As a way of specifying the reference frame, we often say object $A$ is moving relative to object $B$, instead of specifying explicitly a reference frame $F_B$ that is attached to object $B$.
Modified 2018-06-22 by Andrea Censi
Suppose there are two cars A and B both moving at 60 miles per hour eastward. When saying this, we implicitly assume the reference frame of the ground. In the ground’s reference frame, the ground itself is at rest, car A and car B are both moving at 60 miles per hour eastward. In car A’s reference frame, however, car B is at rest and the ground is moving 60 miles per hour westward!
Modified 2018-06-22 by Andrea Censi
To simplify the following discussion, we additionally assume that we choose reference frames such that their axes are parallel. In order to translate motions between reference frames, we assume two rules.
Exercise to readers: derive these rules from kinematics.
As a corollary to the first rule, we immediately derive that frame $R$ is at rest relative to itself, since $\avec{0}$ is the only vector is also its own opposite.
Exercise to readers: translate car B’s motion relative to the ground to relative to car A.
Maintainer: Falcon Dai
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