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Confused by radial vs. centripetal acceleration

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eventob
#1
Dec5-10, 08:26 AM
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.
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Doc Al
#2
Dec5-10, 08:32 AM
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Quote Quote by eventob View Post
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.
eventob
#3
Dec5-10, 08:35 AM
P: 32
Thank you very much. :)

K^2
#4
Dec5-10, 02:38 PM
Sci Advisor
P: 2,470
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.

[tex]a_r = a_c + \ddot{r} = -\omega^2 r + \frac{d^2r}{dt^2}[/tex]

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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