2053Lecture9 - Rotational Motion Topics of Discussion...

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Unformatted text preview: Rotational Motion Topics of Discussion Angular Measurement Average Angular Velocity & Acceleration Instantaneous Angular Velocity & Acceleration Relationship between Linear & Angular Quantities Rotational Motion Rotational Systems A rotational system is described in terms of the angular displacement , the angular velocity and the angular acceleration of a body. The variables , and are called the state variables of the rotational system. Rotational System , , Geometry & Angular Measurement Given a circle of radius r, the angle subtending a length s along the circumference of the circle is given by =s/r. Angular measurement is given in the dimensionless SI unit of the radian. Angular measurement can also be expressed in the revolution or the degree by noting that 2 radians = 1 rev = 360. Average Angular Speed & Acceleration Let the initial time, the initial angular displacement and the initial angular velocity be written as ti, i and i. Let the final time, the final angular displacement the and final angular velocity be written as tf, f and f. Then the average angular velocity and the average angular acceleration is given by f -i f -i = = = and = . t t f - ti t t f - ti Instantaneous Angular Speed & Acceleration Suppose the time interval t is very small. The instantaneous angular velocity is f -i = lim = lim . t 0 t t 0 t - t f i The instantaneous angular acceleration is f -i = lim = lim . t 0 t t 0 t - t f i A Relationship between Angular & Linear Measurement Let r be the radius of a circular path. Then the linear (tangential) speed vT is related to the angular speed by vT=r. Similarly, the linear (tangential) acceleration aT is related to the angular acceleration by aT=r. A Comparison of Linear & Rotational Motion Linear Motion v = v 0 + at 1 x = ( v0 + v ) t 2 1 2 x - x 0 = v 0 t + at 2 2 2 v = v 0 + 2a ( x - x 0 ) Rotational Motion = 0 + t 1 = ( 0 + ) t 2 1 2 - 0 = 0t + t 2 2 2 = 0 + 2 ( - 0 ) ...
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