What is the Relationship Between Radius and Centripetal Acceleration?

[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

 

[Kurdt]

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.

 

[Mindscrape]

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.

 

[Kurdt]

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.