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: ˆ t υ υ = G Direction - velocity is tangent to the path, so υ G is directed along the + t axis. Magnitude (speed) - 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 – change in magnitude of velocity (speed): t d a dt υ = . Normal acceleration – change in direction of velocity: 2 n a R υ = R = radius of curvature Circular motion 2 radius of the circle t n rad R d a dt a a R υ υ = = = = Uniform circular motion: υ = constant 2 2 2 2 2 : period in sec, : frequency in 0 2 2 4 4 Hz t n rad a R R f T R a a R f R T f T π υ π υ π π = = = = = = = NOTE: In circular motion, the normal acceleration is always pointing toward the center of the circle, so it is also referred to as the centripetal acceleration or radial acceleration ( a rad ). 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
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