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Relative Velocity in 2D

Find the magn...

Question

Find the magnitude of displacement of a particle moving in a circle of radius $r$ of constant angular sped $w$ as a function of time $t$

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Solution

Particle is at the extreme left of diameter
$x = a c o s ϕ y = a s i n ϕ r = \sqrt{{(a + a c o s ϕ)}^{2} + {(a s i n ϕ)}^{2}} = a \sqrt{1 + {cos}^{2} ϕ + 2 c o s ϕ + {sin}^{2} ϕ} = a \sqrt{2} \sqrt{2} c o s \frac{ϕ}{2} = 2 a c o s (\frac{ϕ}{2}) m a g n i t u d e o f d i s p l a c e m e n t w h i c h i s r = 2 a c o s (\frac{ϕ}{2}) = 2 a c o s (\frac{ω t}{2})$

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