Speed

In this question, the average tangential speed along the circular path is being calculated by the following formula:\[\text{Average tangential speed} = \frac{\text{Total circular distance travelled}}{\text{Total time taken}}\]The Singapore Flyer is one of the world’s most famous Ferris wheels, which has a radius of \(75\) m.

1. Given that it takes \(30\) minutes for the Singapore Flyer to finish one full rotation, find the average tangential speed of the Singapore Flyer in one full rotation in m/s.
2. Find the average speed of ascending in vertical direction, for a capsule of the Singapore Flyer to travel from the lowest point to the highest point.

The London Eye is another famous Ferris wheel in the world, which also finishes one full rotation in \(30\) minutes.

3. Given that the ratio of the radius of the Singapore Flyer to the radius of the London Eye is \(5 : 4\), find the average tangential speed of the London Eye in one full rotation in m/s.
4. Using your answer in (iii), find the average speed of descending in vertical direction, for a capsule of the London Eye to travel from the highest point to the lowest point.

Use the stated dimensions as a mathematical model and assume both wheels rotate uniformly. Then a half-turn takes half the full-turn time.