# What is the Relationship Between Radius and Centripetal Acceleration?

• chemspy
In summary, the relationship between radius and centripetal acceleration is inverse. This can be seen in the equations ac= v^2/r and ac=4pi^2R/T^2, where the first expression contains more hidden radius terms. However, in different contexts, the relationship can also be direct, as seen in the second equation which relates acceleration to both radius and angular velocity. Ultimately, the relationship between radius and centripetal acceleration depends on the specific situation and should not be solely determined by equations.
chemspy
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

the second expression comes from the fact that $$v=r\omega$$ and $$\omega= \frac{2\pi}{T}$$. 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.

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A puzzling relationship refers to a relationship between two or more variables or factors that is not easily understood or explained. It is often characterized by conflicting or unexpected patterns or results, making it difficult to draw clear conclusions.

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