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):

http://img198.imageshack.us/img198/5021/thedifferencebetween.jpg 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]

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.

 

[Doc Al]

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.

 

[tiny-tim]

Hi Femme_physics!

See also http://en.wikipedia.org/wiki/Polar_coordinate_system#Vector_calculus"

(oh, and centripetal acceleration is minus radial acceleration)

 

[Andrew Mason]

(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

 

[tiny-tim]

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

 

[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]

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.