The distance from the center of a Ferris wheel to a passenger seat is 6.0 m. What centripetal acceleration does a passenger experience when the wheel rotates once every 4π seconds?Select one:a.3.0 m/s2b.16.9 m/s2c.9.0 m/s2d.1.5 m/s2
Question
The distance from the center of a Ferris wheel to a passenger seat is 6.0 m. What centripetal acceleration does a passenger experience when the wheel rotates once every 4π seconds?Select one:a.3.0 m/s2b.16.9 m/s2c.9.0 m/s2d.1.5 m/s2
Solution
The centripetal acceleration can be calculated using the formula:
a = ω²r
where: ω is the angular velocity, r is the radius of the circle.
First, we need to find the angular velocity. The angular velocity is the rate of change of the angle with respect to time. It can be calculated using the formula:
ω = 2π/T
where: T is the period of rotation.
Given that the Ferris wheel rotates once every 4π seconds, the period T is 4π seconds.
So, ω = 2π/(4π) = 0.5 rad/s
Now, we can substitute ω = 0.5 rad/s and r = 6.0 m into the formula for centripetal acceleration:
a = ω²r = (0.5 rad/s)² * 6.0 m = 1.5 m/s²
So, the centripetal acceleration a passenger experiences when the wheel rotates once every 4π seconds is 1.5 m/s². Therefore, the correct answer is d. 1.5 m/s².
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