# 6.3.1 The Ferris Wheel

So far, we have been studying circular motion in horizontal planes. We are now going to look at vertical circular motion.

Take for example the Singapore Flyer, a gigantic ferris wheel that rotates at a constant speed. If you are standing in one of the capsules, you will automatically be undergoing uniform circular motion. Only three forces are acting on you: downward weight mg, upward normal contact force N, and horizontal frictional force f. The resultant of these three forces must always be in the centripetal direction i.e. towards the center of the wheel.

But as the ferris wheel rotates, the centripetal direction changes continuously. At the 6 o’clock, 9 o’clock, 12 o’clock and 3 o’clock positions, the centripetal directions are upward, rightward, downward and leftward respectively. Because of this, both N and f vary in magnitude continuously during the rotation.

Normal contact force

The maximum value of N occurs at the bottom, where N must be larger than mg by the amount $mr{{\omega }^{2}}$ to provide the required upward centripetal force. The minimum value of N occurs at the top, where N must be smaller than mg by the amount $mr{{\omega }^{2}}$ to result in the required downward centripetal force.

Frictional force

The maximum value of f occurs at the 3 o’clock and 9 o’clock positions, where it is the sole provider of the required $mr{{\omega }^{2}}$ in the horizontal direction, and zero at the 6 o’clock and 12 o’clock positions, where it plays no role in the required $mr{{\omega }^{2}}$ in the vertical direction.

Other positions

99% of the time, H2 syllabus only tests students on those four positions. Once in a blue moon, we will venture into other positions. Not to worry, it is not that difficult. Take for example the 7 o’clock position, where the centripetal direction is 60° above the horizontal. As such the net force must also be directed both upward and rightward.

Vertically:        $N-mg=mr{{\omega }^{2}}\cos 30{}^\circ$

Horizontally:    $f=mr{{\omega }^{2}}\sin 30{}^\circ$

Video Explanation

Ferris Wheel