Transcription of Circular Motion Tangential & Angular Acceleration
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Circular Motion Tangential & Angular Acceleration
Rick Field 2/6/2014 University of FloridaPHY 2053 Page 1 Circular MotionTangential & Angular Acceleration rvt=The arc length s is related to the angle (in radians = rad) as follows: Tangential Acceleration : rs= tradialtradialtotaraaaa+ =+=rrr rdtdrdtdvatt===dtdtt = = 0lim(radians/s2) Overall Acceleration : Tangential VelocityThe Tangential velocity vtis related to the Angular velocity as follows: The Tangential Acceleration atis related to the Angular Acceleration as follows: at ar Radial Axis r rvt=tv22tradialtottotaaaa+==rRadial AccelerationTangential AccelerationRick Field 2/6/2014 University of FloridaPHY 2053 Page 2 at ar Radial Axis rAngular Equations of Motion Angular Equations of Motion (constant ): 22100)(ttt ++=()0202)(2)( = ttIf the Angular Acceleration is constant thentt +=0)( =)(tRadial AccelerationTangential Acceleration22100)(tatvststt++=tavtvttt+ =0)( rtat=)(()0202)(2)(stsavtvttt = )()(2trtaradial =rtvtatradial/)()(2=(radians/s2)(m/s2)(r adians/s)(radians)(m/s)(m)(m/s2)(m/s2)Ri ck Field 2/6/2014 University of FloridaPHY 2053 Page 3 Angular Equations of Motion Angular Equations of Motion (constant ): 22100)(ttt ++=()0202)(2)( = ttLet N = Number of revolutions (rev)t
Feb 06, 2014 · Angular Equations: Examples • A disk rotates about its central axis starting from rest at t = 0 and accelerates with constant angular acceleration. At one time it is rotating at 4 rev/s; 60 revolutions later, its angular speed is 16 rev/s. Starting at t = 0, what is the time required to complete 64 revolutions? Answer: t = 8 seconds
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