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Ex_2Dmotion_nt - 2-D Motion in n-t coordinates Velocity...

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2-D Motion in n-t coordinates Velocity: velocity is tangent to the path, so υ G is directed along the + t axis. Acceleration: 22 ˆ ˆ tn t aa ta n a a a =+ = + G n Tangential acceleration: t d a dt = . Normal acceleration: 2 n a R = R = radius of curvature Circular motion 2 , radius of the circle ( : radial acceleration) r a d r a d d aR a dt R υυ == = = Uniform circular motion: υ = constant 2 24 0 , 2 , 4 r a d RR f a a TR T πυ π υπ === = = = = R f Example The Ferris wheel has a 12 m radius and rotates clockwise as shown. (a) If the wheel is rotating at a constant rate with four turns every minute, find the magnitude and direction of the acceleration of the rider at
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