# Confused by radial vs. centripetal acceleration

by eventob
 P: 32 Hi I've been working through some examples from the course material we use in physics class, but one thing keeps confusing me: What is the difference between centripetal and radial acceleration? For instance, when we have a particle traveling in a circular path, the acceleration towards the center of the circle may be written as Ar (a sub r)=-Ac= - v^2/r, while other times it is written simply as Ac=v^2/r. The text book (JS Physics for Scientists and Engineers) seems to use both. Where is the negative sign coming from? I made a quick sketch. Am I right if i think that the radial acceleration is negative in the first circle (to the left) and it is positive in the circle to the right? Is it just due to how I pick the axis and how I define positive direction? Thanks in advance. Attached Thumbnails
Mentor
P: 40,240
 Quote by eventob but one thing keeps confusing me: What is the difference between centripetal and radial acceleration?
Same thing.
 For instance, when we have a particle traveling in a circular path, the acceleration towards the center of the circle may be written as Ar (a sub r)=-Ac= - v^2/r, while other times it is written simply as Ac=v^2/r. The text book (JS Physics for Scientists and Engineers) seems to use both.
v^2/r is the magnitude of the radial acceleration; the direction is toward the center. Whether that's positive or negative just depends on how you define your sign convention.

 Where is the negative sign coming from? I made a quick sketch. Am I right if i think that the radial acceleration is negative in the first circle (to the left) and it is positive in the circle to the right? Is it just due to how I pick the axis and how I define positive direction?
Yes.
 P: 32 Thank you very much. :)
P: 2,406

## Confused by radial vs. centripetal acceleration

Radial acceleration is equal to centripetal acceleration when the radius remains constant (with a +/- sign depending on definition). If radius changes as a function of time, you have to add the explicit second derivative of radius with respect to time.

$$a_r = a_c + \ddot{r} = -\omega^2 r + \frac{d^2r}{dt^2}$$

Similarly, tangential acceleration will pick up a term that depends on the second derivative of angle with respect to time and a Coriolis Effect term.

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