The Cosmo Clock 21 Ferris wheel in Yokohama, Japan, has a diameter of 100 m. Its name comes from its 60 arms, each of which can function as a second hand (so that it makes one revolution every 60.0 s). (a) Find the speed of the passengers when the Ferris wheel is rotating at this rate.

Verified step by step guidance

1. First, understand that the speed of the passengers on the Ferris wheel is the linear speed along the circular path. This can be calculated using the formula for the circumference of a circle and the time for one complete revolution.
2. Calculate the circumference of the Ferris wheel using the formula: \( C = \pi \times d \), where \( d \) is the diameter of the Ferris wheel. Here, \( d = 100 \text{ m} \).
3. Substitute the given diameter into the formula to find the circumference: \( C = \pi \times 100 \text{ m} \).
4. Next, use the relationship between linear speed \( v \), circumference \( C \), and time \( T \) for one complete revolution: \( v = \frac{C}{T} \). Here, \( T = 60.0 \text{ s} \).
5. Substitute the values of \( C \) and \( T \) into the formula to find the linear speed: \( v = \frac{\pi \times 100 \text{ m}}{60.0 \text{ s}} \).

Key Concepts

Circular Motion

Circular motion refers to the movement of an object along the circumference of a circle or rotation along a circular path. In this context, the Ferris wheel rotates in a circular path, and understanding this motion is crucial to determining the speed of the passengers. The key parameters include the radius of the circle and the time taken for one complete revolution.

Circumference of a Circle

The circumference of a circle is the distance around the circle, calculated as C = 2πr, where r is the radius. For the Ferris wheel, with a diameter of 100 m, the radius is 50 m. The circumference is essential for finding the distance a passenger travels in one complete revolution, which is necessary to calculate their speed.

Speed in Circular Motion

Speed in circular motion is the distance traveled per unit of time. For an object moving in a circle, speed can be calculated by dividing the circumference by the time for one complete revolution. In this case, the speed of the passengers is the circumference of the Ferris wheel divided by the 60 seconds it takes to complete one revolution.