LN_Sec_12-4_12-5 - CURVILINEAR MOTION: RECTANGULAR...

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CURVILINEAR MOTION: RECTANGULAR COMPONENTS (Sections 12.4-12.5) Today’s Objectives : Students will be able to: a) Describe the motion of a particle traveling along a curved path. b) Relate kinematic quantities in terms of the rectangular components of the vectors. In-Class Activities : Check homework, if any Reading quiz Applications General curvilinear motion Rectangular components of kinematic vectors Concept quiz Group problem solving Attention quiz
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APPLICATIONS The path of motion of each plane in this formation can be tracked with radar and their x, y, and z coordinates (relative to a point on earth) recorded as a function of time. How can we determine the velocity or acceleration of each plane at any instant? Should they be the same for each aircraft?
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APPLICATIONS (continued) A roller coaster car travels down a fixed, helical path at a constant speed. How can we determine its position or acceleration at any instant? If you are designing the track, why is it important to be able to predict the acceleration of the car?
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POSITION AND DISPLACEMENT A particle moving along a curved path undergoes curvilinear motion . Since the motion is often three-dimensional, vectors are used to describe the motion. A particle moves along a curve defined by the path function, s. The position of the particle at any instant is designated by the vector r = r (t). Both the magnitude and direction of r may vary with time. If the particle moves a distance s along the curve during time interval t, the displacement is determined by vector subtraction : r = r’ - r
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VELOCITY Velocity represents the rate of change in the position of a particle. The average velocity of the particle during the time increment t is v avg = r / t . The
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LN_Sec_12-4_12-5 - CURVILINEAR MOTION: RECTANGULAR...

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