Question

Ezra is designing a virtual Ferris wheel for a school project. This Ferris wheel he has designed has a radius of 8 meters. The center of the Ferris wheel is 11 meters above the ground. How fast is the wheel rotating in revolutions per minute?

Answer 1

To find the number of revolutions per minute the Ferris wheel is rotating at, relate the centripetal acceleration to the gravitational acceleration and find the angular speed.

Step-by-step explanation:

To find the number of revolutions per minute the Ferris wheel is rotating at, we need to relate the centripetal acceleration to the gravitational acceleration and find the angular speed.

1. First, we need to find the centripetal acceleration. Since the magnitude of the centripetal acceleration is 1.50 times that due to gravity, we can find it using the equation:
2. Ac = 1.50 * g
3. Next, we can relate the centripetal acceleration to the angular speed (ω) using the formula:
4. Ac = ω^2 * r
5. Substituting the values, we get:
6. 1.50 * g = ω^2 * r
7. Solving for ω, we get:
8. ω = sqrt((1.50 * g) / r)
9. Converting ω to revolutions per minute, we can use the relation:
10. 1 revolution = 2π radians
11. 1 minute = 2π * 60 seconds
12. Multiplying ω by this conversion factor, we can find the number of revolutions per minute.