An important distinction between the rectangular coordinate system and the normal-tangential coordinate system is that the axes are not fixed in the normal-tangential coordinate system. In such cases, we would define ourself as the origin point and "forward" would be the tangential direction. Normal-tangential coordinate systems work best when we are observing motion from the perspective of the body in motion, such as being a passenger in a car or plane. The u-t and u-n vectors represent unit vectors in the t and n directions respectively. The t-direction is the current direction of travel and the n-direction is always 90 degrees counter-clockwise from the t-direction. In the normal-tangential coordinate system the particle itself serves as the origin point. The diagram below shows a particle following a curved path with the current normal and tangential directions. The tangential direction (t-direction) is defined as the direction of travel at that moment in time (the direction of the current velocity vector), with the normal direction (n-direction) being 90 degrees counterclockwise from the t-direction. The origin point will be the body itself, meaning that the position of the particle in the n-t coordinate system is always "zero". The normal-tangential coordinate system centers on the body in motion. Any planar motion can potentially be described with any of the three systems, though each choice has potential advantages and disadvantages. The most common options in engineering are rectangular coordinate systems, normal-tangential coordinate systems, and polar coordinate systems. When analyzing such motion, we must first decide the type of coordinate system we wish to use. Two Dimensional Motion (also called Planar Motion) is any motion in which the objects being analyzed stay in a single plane. Two Dimensional Kinematics in Normal-Tangential Coordinate Systems
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