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Confused by radial vs. centripetal acceleration 
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#1
Dec510, 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. 


#2
Dec510, 08:32 AM

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#3
Dec510, 08:35 AM

P: 32

Thank you very much. :)



#4
Dec510, 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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