Is radial acceleration and centripetal acceleration the same thing?

Femme_physics

In uniform circular motion,

Is radial acceleration and centripetal acceleration the same thing? Just a vector pointing towards the center? i.e. a synonym?

Doc Al

Yes. Typically those terms are synonymous in that context.

Femme_physics

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.

Doc Al

Those formulas are essentially the same. For whatever reason, the second formula uses n for the frequency. (Think n = number of cycles per second.)

Femme_physics

I see it now :) Thanks Doc.

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.

I like Serena

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.

Doc Al

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.

tiny-tim

Hi Femme_physics!

See also http://en.wikipedia.org/wiki/Polar_c...ector_calculus

(oh, and centripetal acceleration is minus radial acceleration)

Andrew Mason

Did you mean to say that the centripetal acceleration direction is opposite to the radial vector?

The accelerations are the same:

[tex]\vec{F_c}/m = -\omega^2r \hat{r} = \ddot{\vec{r}}[/tex]

AM

tiny-tim

Hi Andrew!

(not enough {} )

Yes … eg a centripetal acceleration of 5 m/s² would be a radial acceleration of -5 m/s²

Femme_physics

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!

Doc Al

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.