Is radial acceleration and centripetal acceleration the same thing?

In summary, the accelerations are the same--radial and centripetal--as long as the net force has a tangential component.
  • #1
Femme_physics
Gold Member
2,550
1
In uniform circular motion,

Is radial acceleration and centripetal acceleration the same thing? Just a vector pointing towards the center? i.e. a synonym?
 
Physics news on Phys.org
  • #2
Yes. Typically those terms are synonymous in that context.
 
  • #3
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 [Broken]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.
 
Last edited by a moderator:
  • #4
Those formulas are essentially the same. For whatever reason, the second formula uses n for the frequency. (Think n = number of cycles per second.)
 
  • #5
I see it now :) Thanks Doc.
 
  • #6
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.
 
  • #7
Femme_physics said:
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.
 
  • #8
Femme_physics said:
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.
 
  • #10
tiny-tim said:
(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:

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

AM
 
Last edited:
  • #11
Andrew Mason said:
Did you mean to say that the centripetal acceleration direction is opposite to the radial vector?

The accelerations are the same:

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

AM

Hi Andrew! :smile:

(not enough {} :wink:)

Yes … eg a centripetal acceleration of 5 m/s2 would be a radial acceleration of -5 m/s2 :wink:
 
  • #12
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!
 
  • #13
Femme_physics said:
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.
 

1. Is radial acceleration and centripetal acceleration the same thing?

No, they are not the same thing. While both are types of acceleration that involve circular motion, radial acceleration specifically refers to the change in direction of velocity, while centripetal acceleration refers to the change in speed.

2. What is the formula for calculating radial acceleration and centripetal acceleration?

The formula for radial acceleration is a = v^2/r, where v is the tangential velocity and r is the radius. The formula for centripetal acceleration is a = ω^2r, where ω is the angular velocity and r is the radius.

3. How are radial acceleration and centripetal acceleration related?

Radial acceleration is a component of centripetal acceleration. In circular motion, there is a constant centripetal acceleration towards the center of the circle, which can be broken down into a tangential component (radial acceleration) and a normal component (tangential acceleration).

4. Can an object have radial acceleration but not centripetal acceleration?

No, an object cannot have radial acceleration without also having centripetal acceleration. This is because radial acceleration is a component of centripetal acceleration, and circular motion requires a change in both direction and speed.

5. What are some real-world examples of radial acceleration and centripetal acceleration?

Some examples of radial acceleration include a car turning around a curve, a roller coaster looping around a track, and a planet orbiting around a star. Examples of centripetal acceleration include a ball on a string swinging around in a circle, a satellite orbiting around Earth, and a spinning top.

Similar threads

Replies
21
Views
7K
  • Mechanics
Replies
16
Views
906
Replies
2
Views
885
Replies
2
Views
712
Replies
15
Views
2K
Replies
24
Views
1K
Replies
7
Views
2K
  • Mechanics
Replies
6
Views
2K
Back
Top