ENG 102 Study Guide - Midterm Guide: Gyration, Area Density, Unit Vector
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Taking derivatives in a ref. frame where vector is fixed will result in a zero. In ref frame n w/ unit vector basis (cid:1866)(cid:2869) ,(cid:1866)(cid:2870) , we express (cid:1874) as (cid:1874)(cid:2869)(cid:1866)(cid:2869) +(cid:1874)(cid:2870)(cid:1866)(cid:2870) . If v1 and v2 are constants, then (cid:1874) is fixed in n. A vector that is not fixed in a given ref frame is a fxn of one of more scalar (cid:448)aria(cid:271)les i(cid:374) that fra(cid:373)e (cid:894)e. g. s, (cid:895) If vector is known (magnitude and dir) (b) no easy a(cid:272)(cid:272)ess to : position vector, go parallel to unit vectors (a) if angle is known, use (cid:1874) =(cid:1874)(cid:1855)(cid:1867)(cid:1871)(cid:2869)(cid:1866)(cid:2869) + (cid:1874)(cid:1855)(cid:1867)(cid:1871)(cid:2870)(cid:1866)(cid:2870) . If (cid:1874) is not a position vector, find position unit vectors to (cid:1874) and. |(cid:1843)|=||(cid:1843) (cid:1875) (cid:1857)(cid:1870)(cid:1857) (cid:1843) (cid:1871) (cid:1857)(cid:1876)(cid:1868)(cid:1870)(cid:1857)(cid:1871)(cid:1857)(cid:1856) (cid:1866) (cid:2835) ,(cid:2836) (cid:1863) multiply by magnitude of f. 12 ft = 1 m g = 9. 81 m/s2 = 32. 2 ft/s2 mass = lb/(ft/s2) (cid:1853)(cid:1866)(cid:1864)(cid:1857) (cid:1854)(cid:1857)(cid:1872)(cid:1875)(cid:1857)(cid:1857)(cid:1866) (cid:1874) (cid:1853)(cid:1866)(cid:1856) (cid:1874): Theta is the angle between tail to tail vectors.
