06 - 2D particle kinematics - Motion in n-t coordinates

06 - 2D particle kinematics - Motion in n-t coordinates -...

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2-D Particle Kinematics – Motion in n-t coordinates (1) Velocity: ˆ t υ = G Direction - velocity is tangent to the path, so G is directed along the + t axis. Magnitude (speed) - ds dt = where s is the actual traveling distance along the trajectory (2) Acceleration: 22 ˆ ˆ tn t aa ta n a a a =+ = + G n Tangential acceleration – change in magnitude of velocity (speed): t d a dt = . Normal acceleration – change in direction of velocity: 2 n a R = R = radius of curvature Circular motion 2 radius of the circle t nr a d R d a dt R = = = = Uniform circular motion: υ = constant 2 : period in sec, : frequency in 0 2 2 4 4 Hz t a d a R Rf T R R f R Tf T π υπ = == = = 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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06 - 2D particle kinematics - Motion in n-t coordinates -...

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