particle moves in a circle according to the equation \\(\\bar{r}=cos (t^2)\\hat{i} +sin(t^2)\\hat{j}\\). The magnitude of the normal component of the acceleration at time \\(t\\) is
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Expert's answer
2020-03-19T07:52:48-0400
Let's make sure that the particle really moves around the circle.
(1) r(t)=cos(t2)i^+sin(t2)j^ .
To do this, we find the vector (1) module
(2) ∣r∣=r⋅r=cos2(t2)+sin2(t2)=1
Thus r is the unit vector r=r^ . The particle moves in a circle with unit radius. Find its velocity
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the solution is excellent. thank you