- #1
eric_phsyics
- 2
- 0
What mass is required to keep the seat of a ferris wheel from swinging no more than 30 degrees measured from the vertical axis?
So let's say we have a big ferris wheel with radius R and its spinning at 10 RPM. At the end of the ferris wheel, is a hinge, and a hanging bucket (like the picture). How do we figure out the swinging motion as the wheel rotates?
http://data:image/jpeg;base64,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
On the bucket hinge (where it attaches to the wheel) we have a torque created by gravity, and a centrifugal force from the momentum of the bucket. I can't seem to figure out the geometry though.