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Lecture_3

# Lecture_3 - CURVILINEAR MOTION NORMAL AND TANGENTIAL...

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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 : 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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READING QUIZ 1. If a particle moves along a curve with a constant speed, then its tangential component of acceleration is A) positive. B) negative. C) zero. D) constant. 2. The normal component of acceleration represents A) the time rate of change in the magnitude of the velocity. B) the time rate of change in the direction of the velocity. C) magnitude of the velocity. D) direction of the total acceleration.
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?
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 instant is defined by the distance, s, along the curve from a fixed reference point.
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