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lecture+notes+3 - 14:440:222 Dynamics(Lecture Note#3...

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14:440:222 Dynamics (Lecture Note #3) Instructor: Prof. Peng Song Rutgers University Today’s Lecture •Cu rv i l inea r mo t ion • Normal-tangential ( n-t ) coordinates

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Applications Cars traveling along a clover-leaf interchange experience an acceleration due to a change in velocity as well as due to a change in direction of the velocity. If the car’s speed is increasing at a known rate as it travels along a curve, how can we determine the magnitude and direction of its total acceleration? Why would you care about the total acceleration of the car? A roller coaster travels down a hill for which the path can be approximated by a function y = f(x). The roller coaster starts from rest and increases its speed at a constant rate. How can we determine its velocity and acceleration at the bottom? Why would we want to know these values? Applications (cont’d)
Normal and Tangential Components When a particle moves along a curved path, it is sometimes convenient to describe its motion using coordinates other than Cartesian. When the path of motion is known, normal (n) and tangential (t) coordinates are often used. In the n-t coordinate system, the origin is located on the particle (the origin moves with the particle). The t-axis is tangent to the path (curve) at the instant considered, positive in the direction of the particle’s motion.

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This document was uploaded on 10/31/2011 for the course ENG MECH 232 at Rutgers.

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lecture+notes+3 - 14:440:222 Dynamics(Lecture Note#3...

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