Phy 201: General Physics IRotational Motion & Angular DisplacementRelationship between rotational & linear variables for circular motionCentripetal & Tangential AccelerationPhy 201: General Physics IChapter 8: Rotational KinematicsLecture NotesRotational Motion & Angular Displacement•When an object moves in a circular path (or rotates):–It remains a fixed distance (r) from the center of the circular path (or axis of rotation)–Since radial distance is fixed, position can be described by its angular position ()•Angular position () describes the position of an object along a circular path–Measured in radians (or degrees)•Angular displacement:•Angular velocity: the rate at which angular position changes:•Angular acceleration: is the rate at which angular velocity changes:θω = tDD{ }fi iθ = θ - θ = θ when θ is 0Dω = taDDRelationship between rotational & linear variables for circular motionPosition:WhereDisplacement (arc length): s = rLinear (tangential) speed: vT = rLinear Acceleration: a = rrRWhen to = 0 and is constant:1 - o = t2 - o = ½(o + )t 3 - o = o + ½ t24 2 - o2 = 2Equations of Rotational KinematicsR = θ r�rr( ) ( )ˆ ˆand x = r sinθ x y = r cosθ y� �r rsRiRfCentripetal & Tangential AccelerationFor an object moving in uniform circular motion, the magnitude of its centripetal acceleration is:Since v = r v2 = ( r)2 therefore:ac = 2rWhen is not constant, the effect of angular acceleration must also included:Or Thus, an object’s circular motion can be generalized in terms of and Notes:1. The 2 components of acceleration are perpendicular to each other2. To determine the magnitude & direction of a, they must be treated as vectors( ) ( )ˆ ˆc a = -a r + r r a^Pr( )( )ˆ ˆ2 a = -ω r r + r r a^Pr2cva
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