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12-7 - CURVILINEAR MOTION NORMAL AND TANGENTIAL COMPONENTS...

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CURVILINEAR MOTION: NORMAL AND TANGENTIAL COMPONENTS Today’s Objectives : Students will be able to: 1. Determine the normal and tangential components of velocity and acceleration of a particle traveling along a curved path. In-Class Activities : Check Homework Reading Quiz Applications Normal and Tangential Components of Velocity and Acceleration Special Cases of Motion Concept Quiz Group Problem Solving Attention Quiz
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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?
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APPLICATIONS (continued) 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?
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NORMAL AND TANGENTIAL COMPONENTS (Section 12.7) 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. The n-axis is perpendicular to the t-axis with the positive direction toward the center of curvature of the curve.
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NORMAL AND TANGENTIAL COMPONENTS (continued) The position of the particle at any
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