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lecture+notes+4 - 14:440:222 Dynamics (Lecture Note #4)...

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14:440:222 Dynamics (Lecture Note #4) Instructor: Prof. Peng Song Rutgers University Today’s Lecture •Cu rv i
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Applications Cylindrical Components We can express the location of P in polar coordinates as r = r u r . Note that the radial direction, r, extends outward from the fixed origin, O, and the transverse coordinate, ! is measured counter- clockwise (CCW) from the horizontal.
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Velocity in Polar Coordinates Velocity in Polar Coordinates The instantaneous velocity is defined as: v = d r /dt = d(r u r )/dt v = r u r + r d u r dt . Using the chain rule: d u r /dt = (d u r /d )(d /dt) We can prove that d u r /d = u ± so d u r /dt = u ± Therefore: v = r u r + r u ± " " " " " " " Thus, the velocity vector has two components: r, called the radial component, and r called the transverse component. The speed of the particle at any given instant is the sum of the squares of both components or v = (r # 2 r ) 2
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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+4 - 14:440:222 Dynamics (Lecture Note #4)...

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