What is the acceleration normal to PC in polar coordinates?

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Homework Help Overview

The discussion revolves around a problem in polar coordinates involving the motion of a point P along a circular path centered at point O, influenced by a force directed towards point C. Participants are exploring the nature of the accelerations involved, particularly radial and tangential components, and the conditions under which such motion is possible.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conservation of angular momentum and question how tangential acceleration arises if the force is directed solely towards C. There are inquiries about the nature of the force and its implications for circular motion, as well as considerations of the relationship between radial and tangential accelerations.

Discussion Status

The discussion is active, with participants offering various interpretations and questioning assumptions about the force and motion. Some guidance has been provided regarding the use of polar coordinates and the need to consider both radial and tangential components of acceleration, but no consensus has been reached on the specifics of the problem.

Contextual Notes

Participants note that the force's magnitude changes along the circular path, raising questions about how this affects the motion. There is also mention of the need for additional equations of motion to fully describe the system, given the unknown nature of the force.

  • #31
In a direction perpendicular to the line joining C and the particle P at any instant ?

How does that help ?
 
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  • #32
Jahnavi said:
In a direction perpendicular to the line joining C and the particle P at any instant ?
Yes. So what equation can you write?
 
  • #33
Jahnavi said:
Please explain how do we infer this from the question .
It was a guess, you do not know the magnitude of the force. But you can see that the radial component is zero, and the tangential part changes sign at C.
You can imagine a force, proportional to the distance between points C and P.
 
  • #34
haruspex said:
Yes. So what equation can you write?

Sorry . I don't know . Can you tell what needs to be done .
 
  • #35
Jahnavi said:
Sorry . I don't know . Can you tell what needs to be done .
I used polar coordinates with origin at C.
In those coordinates, what is the general expression for the acceleration normal to PC?
 

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