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Unformatted text preview: EQUATIONS OF MOTION: CYLINDRICAL COORDINATES Today ` s Objectives: Students will be able to: 1. Analyze the kinetics of a particle using cylindrical coordinates . InClass Activities: Reading Quiz Applications Equations of Motion Using Cylindrical Coordinates Angle Between Radial and Tangential Directions Concept Quiz Group Problem Solving Attention Quiz READING QUIZ 1. The normal force which the path exerts on a particle is always perpendicular to the _________ A) radial line. B) transverse direction. C) tangent to the path. D) None of the above. 2. When the forces acting on a particle are resolved into cylindrical components, friction forces always act in the __________ direction. A) radial B) tangential C) transverse D) None of the above. APPLICATIONS The forces acting on the 100lb boy can be analyzed using the cylindrical coordinate system. How would you write the equation describing the frictional force on the boy as he slides down this helical slide? APPLICATIONS (continued) When an airplane executes the vertical loop shown above, the centrifugal force causes the normal force (apparent weight) on the pilot to be smaller than her actual weight. How would you calculate the velocity necessary for the pilot to experience weightlessness at A ? CYLINDRICAL COORDINATES (Section 13.6) This approach to solving problems has some external similarity to the normal &amp; tangential method just studied. However, the path may be more complex or the problem may have other attributes that make it desirable to use cylindrical coordinates. Equilibrium equations or l Equations of Motion z in cylindrical coordinates (using r, , and z coordinates) may be expressed in scalar form as: F r = ma r = m (r r 2 ) F = ma = m (r 2 r ) F z = ma z = m z . . . .. .. .. Note that a fixed coordinate system is used, not a l body centered z system as used in the n t approach....
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 Spring '11
 PENGSONG

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