= Solution
On this <circle> the radial coordinate is constant, $r=2$, so \b[$\dot r=\ddot r=0$]. The <velocity> is a <tangent vector> to the <circle> in the anticlockwise direction, represented by $ie^{i\theta}$ when $\dot\theta>0$. Substituting into part (b),
$$
\boxed{\dot z=2i\dot\theta e^{i\theta},\qquad
\ddot z=(-2\dot\theta^2+2i\ddot\theta)e^{i\theta}.}
$$
The inward component is the <centripetal acceleration>; the transverse component allows the <speed> to change. Anticlockwise motion does \b[not] imply uniform <speed> or $\ddot\theta=0$. The preceding figure includes the required tangent arrow.
Back to article page
