Acceleration of a ferris wheel

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Discussion Overview

The discussion revolves around the acceleration of a ferris wheel undergoing uniform circular motion, specifically addressing the nature of tangential acceleration and the forces acting on a rider. Participants explore the definitions and implications of uniform circular motion in relation to gravitational forces and net acceleration.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about why a ferris wheel in uniform circular motion cannot have tangential acceleration, seeking clarification.
  • Another participant states that the acceleration due to gravity is separate from tangential acceleration, which is defined as zero in uniform circular motion.
  • A different participant questions whether gravity has a tangential component, noting that it does except at the top and bottom of the motion, while also mentioning that the net force is centripetal.
  • Some participants request further elaboration on the separation of gravitational acceleration from tangential acceleration, indicating that this distinction may depend on the specific context of the problem.
  • One participant asserts that the forces acting on the object include gravity and the normal force from the seat, emphasizing that these forces must equal the mass times the acceleration, which is directed toward the center in uniform circular motion.
  • Another participant reiterates that the normal force and friction adjust continuously to ensure the net force provides the required centripetal acceleration.

Areas of Agreement / Disagreement

Participants exhibit a mix of agreement and disagreement regarding the nature of tangential acceleration and the role of gravitational forces. Some participants agree on the definition of uniform circular motion having zero tangential acceleration, while others raise questions about the implications of gravitational forces.

Contextual Notes

There are unresolved aspects regarding the specific definitions and contexts in which gravitational forces are considered separate or not, as well as the implications of these distinctions on the overall understanding of forces in uniform circular motion.

nashsth
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Hi everyone I am confused about the acceleration of a ferris wheel undergoing uniform circular motion. By definition, the wheel undergoing uniform circular motion can't have a tangential acceleration, but I am confused as to why. I attached a diagram below to show you what I mean. Could you please clarify this confusion?

Thanks! :-)

https://www.flickr.com/photos/132657700@N04/22089785996/in/dateposted-public/
 
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Welcome to PF!

The acceleration due to gravity is separate, always in the same direction (only tangential twice per revolution) and so not part of the tangential acceleration due to uniform circular motion (which, as you say, is by definition zero).
 
I assume that blue dot is, say, a person riding that Ferris wheel undergoing uniform circular motion. Does gravity have a tangential component? Sure (except at top and bottom). But gravity is not the only force acting on the person. The net force will be centripetal.
 
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Hi, could you please expand on what you said? I didn't understand when you said the acceleration due to gravity is separate. :-(
 
nashsth said:
Hi, could you please expand on what you said? I didn't understand when you said the acceleration due to gravity is separate. :-(
Whether it is separate or not really is an issue of what the specific problem is asking you or specific explanation is referring to. There is nothing beyond that: it is either separate or it isn't, because someone wants it to be or doesn't.
 
nashsth said:
I attached a diagram below to show you what I mean.
The force from the wheel on the blue mass has a tangential component, which cancels the tangential component of gravity.
 
nashsth said:
Hi everyone I am confused about the acceleration of a ferris wheel undergoing uniform circular motion. By definition, the wheel undergoing uniform circular motion can't have a tangential acceleration, but I am confused as to why. I attached a diagram below to show you what I mean. Could you please clarify this confusion?

Thanks! :-)

https://www.flickr.com/photos/132657700@N04/22089785996/in/dateposted-public/
We follow Newton's second law to the letter. What are all the forces on the object (the blue dot)? First is gravity, always downward and equal in magnitude to mg, two is the force by whatever seat or harness is in contact with the object. This could include a normal force + friction. These forces must be together equal to the mass m times the acceleration. What is the acceleration? Since the object is moving in uniform circular motion, the acceleration is always toward the center and equal in magnitude to mv^2/r. There is no tangential acceleration in uniform circular motion. So the vector sum of the forces listed above must be equal to the mass times the acceleration. End of story.
 
Chandra Prayaga said:
We follow Newton's second law to the letter. What are all the forces on the object (the blue dot)? First is gravity, always downward and equal in magnitude to mg, two is the force by whatever seat or harness is in contact with the object. This could include a normal force + friction. These forces must be together equal to the mass m times the acceleration. What is the acceleration? Since the object is moving in uniform circular motion, the acceleration is always toward the center and equal in magnitude to mv^2/r. There is no tangential acceleration in uniform circular motion. So the vector sum of the forces listed above must be equal to the mass times the acceleration. End of story.
To further elaborate on what I wrote above, the normal force and the friction will keep adjusting all the time so that their sum, along with gravity, always gives the m tiomes the acceleration toward the center.
 

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