NSCI 1501 Lecture Notes - Lecture 8: Angular Acceleration, Euclidean Vector, Angular Velocity

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A true measure of an angle should involve geometric quantities. Gi(cid:448)e(cid:374) a(cid:374) a(cid:374)gle , (cid:449)e (cid:449)rite a (cid:272)ir(cid:272)le of a(cid:374)(cid:455) radius r (cid:272)e(cid:374)tered at the (cid:448)erte(cid:454) of the a(cid:374)gle. Then we define the measure of the angle, in radians, as the ratio of the arc (s) it subtends over the radius (r). The correspondence between radians (rad) and degrees is obtained as follows: on one hand, a full circle has angle 360 . On the other hand, the arc of length of a full circle is equal to the circumference c = A(cid:374)gular displa(cid:272)e(cid:373)e(cid:374)t: a(cid:374)gular displa(cid:272)e(cid:373)e(cid:374)t is the a(cid:374)gle or, sa(cid:455), a (cid:271)od(cid:455) rotates about an axis. The counter-clockwise direction is taken as positive (+) and the clockwise as negative (cid:894) (cid:895). The a(cid:374)gular (cid:448)elo(cid:272)it(cid:455) is the rate of (cid:272)ha(cid:374)ge of the a(cid:374)gular displa(cid:272)e(cid:373)e(cid:374)t. the a(cid:374)gular a(cid:272)(cid:272)eleratio(cid:374) is the rate of (cid:272)ha(cid:374)ge of the a(cid:374)gular (cid:448)elo(cid:272)it(cid:455)

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