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29. Cylindrical Coordinates

# 29. Cylindrical Coordinates - ME 270 Basic Mechanics I...

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Unformatted text preview: ME 270 - Basic Mechanics I - Group Quiz NamelGroup #: __________.__ Group Members: 1) __ 2) Date: ________ Period: _.___.__ 3) _._.__.___ 4) Given: The rotation of arm OA about point 0 is deﬁned by the relation 6 = 1tt2/8, where 6 is expressed in radians andt in seconds. Collar B slides along the arm in such a way that its distance from point 0 is given by r = 1 + 26 where r is expressed in meters and 6 in radians. Find: (a) Sketch the cylindrical and cartesian unit vectors on the ﬁgure. (b) Determine the angular velocity (6) and angular r- acceleration ( 6 ) of collar B when 6 = 90°. (c) Determine the radial velocity (i) and radial accelera- tion ('r') ofcollar B when 6 = 90°. ((1) Write expressions for the velocity and acceleration vectors of collar B. (e) Express the velocity and acceleration vectors in terms of canesian coordinates (i,j). S____olution: (b) 9': if: at ”=3" %=Zsecg ﬁﬁﬁﬁﬁ; I vgz 3.1+U;+6.5o'0’; a}: (r— ré‘yx +(ré+zré)Zl; #:E —E/)é)]u'2 +E+/)(f)+2 (:04 {7f (6);=+2f 5 Ear”? ...
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