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## Homework Statement

A particle moves with constant speed ν around a circle of radius b, with the circle offset from the origin of coordinates by a distance b so that it is tangential to the y axis. Find the particle's velocity vector in polar coordinates.

## Homework Equations

(dots for time derivatives are a bit off centered)[/B]Position Vector:

**r**= r

**ˆr**

Velocity Vector:

**v**= ˙r

**ˆr**+ r ˙ θ

**ˆθ**

Angular Speed:

ω = ˙ θ →(Integrating with respect to time)→ ωt = θ

v = bω → ω = v/b

## The Attempt at a Solution

I found the equation of the graph to be r = 2bcosθ.

Differentiating with respect to time i get

˙r = -2bsinθ˙ θ → ˙r = -2bωsinωt.

Substituting the into the velocity vector i obtain:

**v**= -2bωsinωt

**ˆr**+ 2bωcosωt

**ˆθ**

**=**-2vsin(vt/b)

**ˆr**+ 2vcos(vt/b)

**ˆθ**

what am i doing wrong here?, the book uses a confusing approach (confusing to me). For the velocity vector they have…

v = −v sin(vt/2b)ˆr + v cos(vt/2b)ˆθ

any help will be greatly appreciated.