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Unformatted text preview: Chapt. 4 Two- and Three-Dimensional Kinematics 45 a) The displacement vector vector r in polar coordinates is vector r = r r , where r is the magnitude of vector r and r is unit vector pointing in the direction of vector r . Differentiate vector r with respect to time t to find vectorv using the product rule, but dont for the moment try to determine what d r/dt is. b) There is a non-rigorous, but valid and convincing way of evaluating d r/dt . Draw a diagram with r and r + r with angle between them. The r and are the changes in, respectively, radial unit vector r and angular of position of the object in time t . With in radians show that r , where recall is always / 2 = 90 clockwise from r . Now show d r dt = , where = d/dt is the angular velocity. The angular velocity is usually in units of radians per unit time....
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- Fall '06