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## Is radial acceleration and centripetal acceleration the same thing?

In uniform circular motion,

Is radial acceleration and centripetal acceleration the same thing? Just a vector pointing towards the center? i.e. a synonym?
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 Mentor Blog Entries: 1 Yes. Typically those terms are synonymous in that context.
 Recognitions: Gold Member Ah, great :) Thanks. Um, while I got your attention Our lecturer gave us 2 formulas (presumably both to tangential speed): I don't understand the difference between those formulas. Our lecturer wrote us that in "industrial usage" f = n (where f is 1/T). But I don't see the connection.

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## Is radial acceleration and centripetal acceleration the same thing?

Those formulas are essentially the same. For whatever reason, the second formula uses n for the frequency. (Think n = number of cycles per second.)
 Recognitions: Gold Member I see it now :) Thanks Doc.
 Recognitions: Gold Member I understand that V is tangential speed, and that acceleration is centripetal acceleration. But is there also a beast known as tangential acceleration? I thought the only two players here are the two mentioned first.

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 Quote by Femme_physics I understand that V is tangential speed, and that acceleration is centripetal acceleration. But is there also a beast known as tangential acceleration? I thought the only two players here are the two mentioned first.
In general a speed V has a tangential and a radial component.
Same thing for acceleration - it has a tangential and a radial component.

The case of circular movement is special in that the acceleration only has a radial (or centripetal) component.
Furthermore, the speed only has a tangential component.

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 Quote by Femme_physics I understand that V is tangential speed, and that acceleration is centripetal acceleration. But is there also a beast known as tangential acceleration?
In the case of non-uniform circular motion there will be tangential acceleration as well as radial acceleration. Uniform circular motion means constant speed, so the tangential acceleration would be zero.
 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor Hi Femme_physics! See also http://en.wikipedia.org/wiki/Polar_c...ector_calculus (oh, and centripetal acceleration is minus radial acceleration)

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 Quote by tiny-tim (oh, and centripetal acceleration is minus radial acceleration)
Did you mean to say that the centripetal acceleration direction is opposite to the radial vector?

The accelerations are the same:

$$\vec{F_c}/m = -\omega^2r \hat{r} = \ddot{\vec{r}}$$

AM

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 Quote by Andrew Mason Did you mean to say that the centripetal acceleration direction is opposite to the radial vector? The accelerations are the same: $$F_c/m = -\omega^2 r\hat r = \ddot{\vec{r}}$$ AM
Hi Andrew!

(not enough {} )

Yes … eg a centripetal acceleration of 5 m/s2 would be a radial acceleration of -5 m/s2
 Recognitions: Gold Member I can see clearly now :) Tangential acceleration only occurs when there's a force applied. Thanks tiny-tim, ILS, Doc, Andrew. Being in mechanics class for the past 4 hours also helped!

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 Quote by Femme_physics Tangential acceleration only occurs when there's a force applied.
Any acceleration--including centripetal--requires a net force. Better to rephrase your statement like this: Tangential acceleration only occurs when the net force has a tangential component.

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