Lecture_4 - CURVILINEAR MOTION: CYLINDRICAL COMPONENTS...

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Unformatted text preview: CURVILINEAR MOTION: CYLINDRICAL COMPONENTS Today ` s Objectives: Students will be able to: 1. Determine velocity and acceleration components using cylindrical coordinates. In-Class Activities: Reading Quiz Applications Velocity Components Acceleration Components Concept Quiz Group Problem Solving Attention Quiz READING QUIZ 1. In a polar coordinate system, the velocity vector can be written as v = v r u r + v u = r u r + r u . The term is called A) transverse velocity. B) radial velocity. C) angular velocity. D) angular acceleration. . . . 2. The speed of a particle in a cylindrical coordinate system is A) r B) r C) (r ) 2 + ( r) 2 D) (r ) 2 + ( r) 2 + ( z) 2 . . . . . . . APPLICATIONS The cylindrical coordinate system is used in cases where the particle moves along a 3-D curve. In the figure shown, the box slides down the helical ramp. How would you find the box ` s velocity components to know if the package will fly off the ramp? CYLINDRICAL COMPONENTS (Section 12.8) We can express the location of P in polar coordinates as r = r u r . Note that the radial direction, r, extends outward from the fixed origin, O, and the transverse coordinate, , is measured counter- clockwise (CCW) from the horizontal. VELOCITY in POLAR COORDINATES) The instantaneous velocity is defined as: v = d r /dt = d(r u r )/dt v = r u r + r d u r dt ....
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Lecture_4 - CURVILINEAR MOTION: CYLINDRICAL COMPONENTS...

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