# What is the final section the spinning wheel stops on at a county fair game?

• eiriyuki
In summary, the problem involves a betting game at a county fair where a spinning wheel decelerates and stops on one of twelve numbered sections, each with an angle of 30˚. Given an initial angular velocity and deceleration, the task is to determine the numbered section where the wheel will stop. Using the equation ω = 2*π*f, where f is revolutions per second, the solution involves finding θ by subtracting 360 degrees from the number of revolutions and then counting 30-degree increments from left to right (counter-clockwise) on the wheel.
eiriyuki
1. At a county fair there is a betting game that involves a spinning wheel. As the drawing shows, the wheel is set into rotational motion with the beginning of the angular section labeled "1" at the marker at the top of the wheel. The wheel then decelerates and eventually comes to a halt on one of the numbered sections. The wheel in the drawing is divided into twelve sections, each of which is an angle of 30˚. Determine the numbered section on which the wheel comes to a halt when the deceleration of the wheel has a magnitude of 0.355 rev/s2 and the initial angular velocity is (a) +1.61 rev/s and (b) +3.17 rev/s.

http://edugen.wiley.com/edugen/courses/crs2216/art/qb/qu/c08/qu_8_32.gif

## Homework Equations

I tried using equation $$\omega$$$$_{2}$$ = $$\omega$$$$^{2}_{o}$$ + 2$$\alpha$$$$\theta$$

## The Attempt at a Solution

I used 0 is omega final, +1.61 (a), and +3.17(b) are omega initials, alpha is 0.355, and theta is my unknown.

For part a, I got 3.65 revolutions and part B I got 14.15 revolutions. I do not know if this is correct so far, but I do not know how to convert from revolutions to degrees.

One revolution is 360 degrees.

ideasrule said:
One revolution is 360 degrees.

Thank you!

However, I did not get the right answer when I converted my answers to degrees and then found the respective spot on the wheel.

To do this, I found subtracted 360 from my answer until I got a number below 360. Then I when by 30's from left to right (counter-clockwise) on the wheel until I landed in the respective box.

Any help with an error please?

ω = 2*π*f, where f is revolution per second. Try this one to find θ.

## 1. How does the Country Fair Spinning Wheel work?

The Country Fair Spinning Wheel is a manually operated spinning wheel that uses a flyer and bobbin mechanism to turn fibers into yarn. The flyer, or spinning wheel, rotates and draws the fibers onto the bobbin, which then winds the fibers into usable yarn.

## 2. What materials can be spun on the Country Fair Spinning Wheel?

The Country Fair Spinning Wheel can spin a variety of fibers, such as wool, cotton, silk, flax, and alpaca. It can also spin blended fibers, allowing for a wide range of yarn textures and colors.

## 3. How do you adjust the tension on the Country Fair Spinning Wheel?

The tension on the Country Fair Spinning Wheel can be adjusted by moving the tension knob, which controls the distance between the flyer and bobbin. This allows for varying degrees of tension, depending on the type of fiber being spun.

## 4. Is the Country Fair Spinning Wheel suitable for beginners?

While the Country Fair Spinning Wheel may seem complex, it is actually a great option for beginners. It is easy to use, with simple mechanics and adjustable settings. Plus, it is a great way to learn the art of spinning yarn.

## 5. How do you maintain and care for the Country Fair Spinning Wheel?

To ensure the longevity of your Country Fair Spinning Wheel, it is important to regularly clean and oil the moving parts. This will keep the wheel running smoothly and prevent any damage. It is also important to store the wheel in a dry, dust-free area when not in use.

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