Lecture_7 - EQUATIONS OF MOTION NORMAL AND TANGENTIAL...

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Unformatted text preview: EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES Today ` s Objectives : Students will be able to: 1. Apply the equation of motion using normal and tangential coordinates . In-Class Activities : • Reading Quiz • Applications • Equation of Motion in n-t Coordinates • Concept Quiz • Group Problem Solving • Attention Quiz READING QUIZ 2. The positive n direction of the normal and tangential coordinates is ____________. A) normal to the tangential component B) always directed toward the center of curvature C) normal to the bi-normal component D) All of the above. 1. The l normal z component of the equation of motion is written as Σ F n =m a n , where Σ F n is referred to as the _______. A) impulse B) centripetal force C) tangential force D) inertia force APPLICATIONS Race tracks are often banked in the turns to reduce the frictional forces required to keep the cars from sliding up to the outer rail at high speeds. If the car ` s maximum velocity and a minimum coefficient of friction between the tires and track are specified, how can we determine the minimum banking angle ( θ ) required to prevent the car from sliding up the track? APPLICATIONS (continued) The picture shows a ride at the amusement park. The hydraulically-powered arms turn at a constant rate, which creates a centrifugal force on the riders. We need to determine the smallest angular velocity of the cars A and B so that the passengers do not loose contact with the seat. What parameters do we need for this calculation? APPLICATIONS (continued) Satellites are held in orbit around the earth by using the earth ` s gravitational pull as the centripetal force – the force acting to change the direction of the satellite ` s velocity. Knowing the radius of orbit of the satellite, we need to determine the required speed of the satellite to maintain this orbit. What equation governs this situation? NORMAL & TANGENTIAL COORDINATES (Section 13.5) When a particle moves along a curved path , it may be more convenient to write the equation of motion in terms of normal and tangential coordinates ....
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This note was uploaded on 02/27/2012 for the course DYNAMICS 440:222 taught by Professor Pengsong during the Spring '11 term at Rutgers.

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Lecture_7 - EQUATIONS OF MOTION NORMAL AND TANGENTIAL...

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