## Position of Point on London Eye Relative to Ground

The London Eye is a giant Ferris wheel with a radius of 67.5m and takes 30 minutes to make a complete rotation. If we take the point on the ground below the centre has the origin, the the coordinates of the centre are
$(0,67.5)$
.
A point on the wheel rotates at the rate
$2 \pi$
per 30 minutes, or
$\frac{2 \pi}{30 \times 60}= \frac{\pi}{900} rads/sec$
. In a times
$t$
the wheel will rotate through an angle
$\theta = \frac{\pi}{900}t$
. The London eye appears to rotate in the clockwise as seen from the other side of the Thames. By convention, clockwise is negatives, so the angle of rotation is
$- \frac{\pi}{900}t$
.
By convention also the horizontal line is taken as the zero angle, so at any times
$t$
, the position of a point that started from the ground at
$t=0$
is
$(67.5sin(- \frac{\pi}{900}t), 67.5-67.5cos(- \frac{\pi}{900}t)$
.