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Unformatted text preview: page 6 of 9 Information Sheets Cartesian unit vectors may be labelled x, y, z or i, j, k s = r = arc length of a circle of radius r swept out by angle ( in radians) = d / d t = v/r = angular velocity or speed; ( v = tangential speed for circular motion) = d / d t = a t /r = angular acceleration with tangential acceleration a t a r = v 2 /r = 2 r = radial (centripetal) acceleration towards the centre v = v + at, = + t (constant a, ) v 2 = v 2 + 2 a ( x- x ) , 2 = 2 + 2 ( - ) (constant a, ) x = x + v t + 1 2 at 2 , = + t + 1 2 t 2 (constant a, ) x = 1 2 ( v + v ) t, = 1 2 ( + ) t (constant a, ) Centre of mass coordinates: x cm = 1 M n X i =1 m i x i , y cm = 1 M n X i =1 m i y i , z cm = 1 M n X i =1 m i z i Moment of Inertia: I = n X i =1 m i r 2 i = Z r 2 dm , Parallel Axis Theorem: I h = I cm + Mh 2 ~ = ~ r ~ F, = rF sin , X = I Kinetic energy = 1 2...
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- Fall '10