2-D Particle Kinematics – Motion in n-tcoordinates (1) Velocity: ˆtυ=GDirection - velocity is tangent to the path, so Gis directed along the +taxis. Magnitude (speed) - dsdt=where sis the actual traveling distance along the trajectory (2) Acceleration: 22ˆˆtntaatan a a a=+⇒=+GnTangential 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 circletnradRdadtR====Uniform circular motion: υ= constant2: period in sec, : frequency in 022 44HztadaRRfTRRfRTfTπυπ=====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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