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Ex_2Dmotion_nt - 2-D Particle Kinematics Motion in n-t...

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2-D Particle Kinematics – Motion in n-t coordinates (1) Velocity: Direction - velocity is tangent to the path, so υ G is directed along the + t axis. Speed (magnitude of velocity) - ds dt υ = where s is the actual traveling distance along the trajectory (2) Acceleration: 2 2 ˆ ˆ t n t a a t a n a a a = + = + G n Tangential acceleration: t d a dt υ = . Normal acceleration: 2 n a R υ = R = radius of curvature Circular motion 2 radius of the circle ( : radial acceleration) rad t n rad d a dt a a R a R υ υ = = = = Uniform circular motion: υ = constant 2 2 2 2 2 0 2 2 4 4 t n rad a R R f T R a a R f R T π υ π υ π π = = = = = = = 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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