_Microsoft_Word_-_Uniform_Circular_Motion_doc_

_Microsoft_Word_-_Uniform_Circular_Motion_doc_ - (constant...

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Unformatted text preview: (constant speed | v(t)| = v and radius | r(t)| = R) v(t) r (t) (t) R Particle Uniform Circular Motion (t) v(t) v Position r(t) dr(t) v(t) = dt and Velocity v(t) dv(t) What is a(t) = ? dt . . . are rotating vectors. dv(t) a(t) = = dt Direction? t lim 0 v t v v(t) v(t+ t) v(t) (. . . or opposite to r(t)) v (Small Angle/Skinny Triangle Approx.) Magnitude? | v| dv |a| = dt = dv dt = t lim 0 v t = t lim v 0 t = v "angular speed" t lim 0 t 14243 d d = v = |v| dt dt d dt -- Holds for any rotating vector (such as v). dr(t) v(t) = dt d d ^ = R ^ = |r(t)| dt dt dv(t) a(t) = dt d d = |v(t)| (- ^) = v r (- ^) r dt dt ...
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