Lets say we have a vector [tex] \vec{A}(t) [/tex] with a constant magnitude [tex] A [/tex]. Thus [tex] \vec{A}(t) [/tex] can only change in direction (rotation). We know that [tex] \frac{d\vec{A}}{dt} [/tex] is always perpendicular to [tex] \vec{A} [/tex]. This is where I become stuck:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \Delta \vec{A} = \vec{A}(t+\Delta t)-\vec{A}(t) [/tex]

[tex] |\Delta \vec{A}| = 2A\sin\frac{\Delta \theta}{2} [/tex].

How do we get the trigonometric expression on the right in the second equation? It looks like some type of half/double angle formula. Eventually we are supposed to get [tex] \vec{A}\frac{d\theta}{dt} [/tex] or the angular velocity of [tex] \vec{A} [/tex]

Thanks

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# Rotating Vectors

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