What is the Relationship Between Radius and Centripetal Acceleration?

  • Thread starter Thread starter chemspy
  • Start date Start date
  • Tags Tags
    Relationship
Click For Summary

Homework Help Overview

The discussion revolves around the relationship between radius and centripetal acceleration in the context of circular motion. Participants are examining two different equations that express centripetal acceleration and are trying to clarify how radius affects this acceleration.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the implications of two equations for centripetal acceleration and questioning whether the relationship between radius and acceleration is direct or inverse. There is an attempt to reconcile different contexts in which these equations apply.

Discussion Status

The discussion is active, with participants offering different perspectives on the relationship between radius and centripetal acceleration. Some suggest that the relationship is inverse, while others argue that it depends on the context of linear versus angular velocity. No consensus has been reached, but various interpretations are being explored.

Contextual Notes

Participants are navigating potential confusion arising from the different forms of the equations and their underlying assumptions about velocity types. There is an acknowledgment that the two equations may not conflict when considered in their respective contexts.

chemspy
Messages
1
Reaction score
0
Still not sure if I understand this:

ac= v^2/r

YET

ac=4pi^2R/T^2

so what is the relationship between radius and centripetal acceleration? direct or inverse?? everyone tells me differently
 
Physics news on Phys.org
the second expression comes from the fact that [tex]v=r\omega[/tex] and [tex]\omega= \frac{2\pi}{T}[/tex]. therefore technically the first expression contains more radius expressions that are hidden within other terms.
 
Inverse. Centripetal acceleration is larger for either greater velocity or smaller radius. Don't concern yourself so much with equations and just picture a mass on the end of a string. When that string is smaller the velocity is going to be larger, and so the inward accerelertion (the centripetal accerlation) will have to be larger too.
 
Well its both really but in different contexts. The first equation relates accelration to radius and LINEAR velocity while the second relates acceleration to the radius and ANGULAR velocity and thus there is no conflict.
 

Similar threads

Replies
16
Views
1K
Replies
12
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
2
Views
2K
Replies
3
Views
3K
  • · Replies 17 ·
Replies
17
Views
9K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K