# How Is Angular Acceleration Calculated for a Speeding Ferris Wheel?

• EthanVandals
In summary: Referring back to your graph, the wheel will complete one full rotation in 5 seconds. If the wheel were to continue to accelerate at this rate, it would take approximately 9.6 seconds for the wheel to complete a full rotation.
EthanVandals

## Homework Statement

If a Ferris Wheel of radius 25 meters is sped up from a linear speed of 2 meters per second to 3 meters per second, what is its angular acceleration if it takes 5 seconds to do this? How long will it take to complete a complete circle if it continues to accelerate at this rate?

C = 2(pi)r

## The Attempt at a Solution

I imagine I could get the second half of this problem fairly easily once I get the first one because I just need to find 50pi and apply the acceleration to it. We've done problems talking about the force of the bars holding the cars up, and problems about centripetal force, but my professor specifically stated the day before spring break that he forgot to teach us about this, so he doesn't expect anything miraculous. I would still like to understand however. I mapped out the concept on a graph (with the velocity on the y-axis and the time on the x axis. If you look at how long it took for the wheel to actually increase its speed by just 1 m/s, you get a slope of 1/5. But how do you translate this into this "angular acceleration" language? And without calculus, is there a way to actually calculate how long a full rotation will take, since the time where it's undergoing its "change" in velocity is unaccounted for at the moment? Thanks!

EthanVandals said:
my professor specifically stated the day before spring break that he forgot to teach us about this, so he doesn't expect anything miraculous.

These equations are valid when the units of angle are radians.
s = rθ (linear distance = radius times angle)
v = rω (linear velocity = radius times angular velocity)
a = rα (linear acceleration = radius times angular acceleration)

These are true for the same reason as the equation you cited: C = 2πr - that is, because the ratio of the circumference to radius of a circle happens to be 2 times π.

## 1. What is the acceleration of a Ferris wheel?

The acceleration of a Ferris wheel depends on its design and size, but typically ranges from 0.1 to 0.3 meters per second squared.

## 2. Why does a Ferris wheel accelerate?

A Ferris wheel accelerates because it is constantly changing its direction of motion, causing a change in velocity and resulting in acceleration.

## 3. How does the acceleration of a Ferris wheel affect the riders?

The acceleration of a Ferris wheel does not have a noticeable effect on riders due to the circular motion and the fact that they are constantly being pushed towards the center of the wheel.

## 4. What factors determine the acceleration of a Ferris wheel?

The acceleration of a Ferris wheel is determined by its size, the distance between riders and the center of the wheel, and the speed at which it rotates.

## 5. Can the acceleration of a Ferris wheel be changed?

Yes, the acceleration of a Ferris wheel can be changed by adjusting the speed at which it rotates or by changing the size and design of the wheel itself.

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