# Ferris Wheel: Find Direction of Passenger's Acceleration

• rsala
Just turn your picture 90 degrees and you'll see it.In summary, the Ferris wheel in the figure rotates counterclockwise and is just starting up. At a given instant, a passenger on the rim of the wheel is moving at 3.00 m/s and is gaining speed at a rate of 0.500 m/s^2. The radius of the wheel is 14m. The direction of the passenger's acceleration at this instant is 37.9 degrees to the right of the vertical axis.
rsala

## Homework Statement

The Ferris wheel in the figure View Figure , which rotates counterclockwise, is just starting up. At a given instant, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3.00 m/s and is gaining speed at a rate of 0.500 \;{\rm m}/{\rm s}^{2} .

find the direction of the passenger's acceleration at this instant.
the answer must be in degrees from the right of the vertical axis. edited.

## Homework Equations

a$$^{ }_{centripetal}$$ = $$\omega$$$$^{2}_{}$$ x R
or
a$$^{ }_{centripetal}$$ = v$$^{2}_{}$$ / R

## The Attempt at a Solution

since the instant they are referring to is the the lowest point of the ferris wheel (i think)
the centripetal acceleration there is .643 m/s^2 direction is directly upwards...so there's a magnitude of .643 in the y direction with 0 in the x direction there.

since the ferris wheel is accelerating counterclockwise @ .5 m/s^2 the tangential acceleration is .5. with direction to the direct right on the x axis, with 0 magnitude in the y.

this is the point at which i do not understand.
my normal approach to this problem would be to acknowledge that I am finding A, and A = Ax + Ay...Ax = the tangential, and Ay = the centripetal.

and proceed by just pluging the calculator ARCTAN Ay / Ax (which is arctan.643/.5 = arctan1.286)= .90...impossible IT CANT be .90 degrees (nor .9 radians because that's still 52 degrees and not the correct answer)

the correct answer is in fact 37.9 degrees,, how can i find the solution? thanks and sorry for the long read.

the answer must be in degrees from the right of the vertical axis. edited.

Last edited:
You never quite got around to stating the actual question. What is it exactly? I do note that the 'incorrect answer' of 52.1 degrees and the 'correct answer' of 37.9 degrees add up to 90. Interesting coincidence, yes?

i forgot to state that the answer must be in degrees from the right of the vertical axis. edited.

is the 52 degrees that I am getting from the positive x axis?

ive drawn up a photo of what I am thinking, i am not sure if how I am picturing the "degrees to the right of vertical" correctly as the problem wants.

http://img225.imageshack.us/img225/4088/rightfromverticalfromhofz4.jpg

Last edited by a moderator:
rsala said:
i forgot to state that the answer must be in degrees from the right of the vertical axis. edited.

is the 52 degrees that I am getting from the positive x axis?

Yes. Exactly.

ah i get it now, disregard my picture i see where i messed up

rsala said:
i forgot to state that the answer must be in degrees from the right of the vertical axis. edited.

is the 52 degrees that I am getting from the positive x axis?

ive drawn up a photo of what I am thinking, i am not sure if how I am picturing the "degrees to the right of vertical" correctly as the problem wants.

http://img225.imageshack.us/img225/4088/rightfromverticalfromhofz4.jpg
[/URL]

The 37.9 degree angle you should be picturing is the one between the acceleration vector (the one that the 52.1 degree angle is measuring and the vertical axis. I'm not sure why you drew it between the vertical axis and some downward pointing vector.

Last edited by a moderator:

## 1. How does the Ferris Wheel determine the direction of the passenger's acceleration?

The Ferris Wheel uses the laws of motion and the concept of centripetal acceleration to determine the direction of the passenger's acceleration. As the wheel rotates, the passengers experience a change in velocity, which results in an acceleration towards the center of the wheel.

## 2. Why is it important to know the direction of the passenger's acceleration on a Ferris Wheel?

Knowing the direction of the passenger's acceleration is important for understanding the forces acting on the passengers and the potential risks involved. It also helps in designing and maintaining the Ferris Wheel to ensure the safety and comfort of the passengers.

## 3. Can the direction of the passenger's acceleration on a Ferris Wheel change?

Yes, the direction of the passenger's acceleration can change as the Ferris Wheel rotates. This is because the acceleration is always directed towards the center of the wheel, and as the wheel rotates, the direction of the center changes, resulting in a change in the direction of acceleration.

## 4. Is the direction of the passenger's acceleration the same as the direction of the Ferris Wheel's rotation?

No, the direction of the passenger's acceleration and the direction of the Ferris Wheel's rotation are not always the same. While the Ferris Wheel rotates in a circular motion, the direction of the passenger's acceleration is always towards the center of the wheel, regardless of the direction of rotation.

## 5. How does the direction of the passenger's acceleration on a Ferris Wheel affect their experience?

The direction of the passenger's acceleration can affect their experience on a Ferris Wheel by creating a sense of weightlessness or a feeling of being pushed towards the center of the wheel. This can add to the excitement and thrill of riding a Ferris Wheel.

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