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A Ferris wheel with a radius of 9.5 m rotates a constant
Chapter 10, Problem 39P(choose chapter or problem)
A Ferris wheel with a radius of 9.5 m rotates at a constant rate, completing one revolution every 36 s. Find the direction and magnitude of a passenger’s acceleration when (a) at the top and (b) at the bottom of the wheel.
Questions & Answers
QUESTION:
A Ferris wheel with a radius of 9.5 m rotates at a constant rate, completing one revolution every 36 s. Find the direction and magnitude of a passenger’s acceleration when (a) at the top and (b) at the bottom of the wheel.
ANSWER:
Step 1 of 2
Part a
We are required to calculate the magnitude and direction of the passenger's acceleration at the top of the wheel.
Given:
The radius of the wheel \(r=9.5 \mathrm{~m}\)
The wheel completes one revolution in 36 seconds.
Therefore, the angular speed is,
\(\begin{aligned}\omega=(1 / 36)_{\text {rev/s }} \\\omega=2 \pi / 36_{\text {rps }}(\text { since } 1 \mathrm{rev}=2 \pi \text { rotations }) \\\omega=\pi / 18 \mathrm{rps} \\\omega=0.174 \mathrm{rps}\end{aligned}\)