Question

Calculate the angular velocity in radians per minute of a Ferris wheel 250 ft in diameter that takes 45 s to rotate once. Express the answer in terms of Pi.

Answer 1

To calculate the angular velocity in radians per minute, divide the circumference of the Ferris wheel by the time taken to rotate once, and then convert from seconds to minutes. In this case, the angular velocity of the Ferris wheel with a diameter of 250 ft and a rotation time of 45 seconds is (125π ft) / (9 min).

Step-by-step explanation:

To calculate the angular velocity in radians per minute, we need to convert the time it takes to rotate once from seconds to minutes. Given that the Ferris wheel takes 45 seconds to rotate once and has a diameter of 250 ft, we first need to find the circumference of the wheel. The circumference can be calculated using the formula C = π * D, where D is the diameter. So, C = π * 250 ft. Once we have the circumference, we can calculate the angular velocity by dividing the circumference by the time taken to rotate once, and then converting from seconds to minutes.

Let's calculate:

C = π * 250 ft = 250π ft

• Angular velocity = C / time taken to rotate once
• Angular velocity = (250π ft) / (45 s)
• Angular velocity = (250π ft) / (45 s) * (1 min / 60 s)
• Angular velocity = (125π ft) / (9 min)

Therefore, the angular velocity of the Ferris wheel in radians per minute is (125π ft) / (9 min).