2-D Particle Kinematics – Motion in n-tcoordinates (path coordinates) (1) Velocity: ˆtυυ=Direction - velocity is tangent to the path, so υis directed along the +taxis. Magnitude (speed) - dsdt=where sis the actual traveling distance along the trajectory (2) Acceleration: 22ˆˆtntna at anaaa=+ ⇒=+Tangential acceleration – change in magnitude of velocity (speed): tdadt=. Normal acceleration – change in direction of velocity: 2naR=R= radius of curvature − Circular motion 2radius of the circletnradRdadtaaR====Uniform circular motion: υ= constant2: period in sec, : frequency in 022 44HztnradaRRfTRaaRTfTπυπ=======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 (arad).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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This note was uploaded on 10/02/2011 for the course AERO 1234 at Virginia Tech.