# Can centripetal and centrigugal force act together?

1. Oct 14, 2009

### monty37

can centripetal and centrigugal force act together?

2. Oct 14, 2009

### Staff: Mentor

Realize that in standard physics usage "centrifugal force" refers to a fictitious (or inertial) force that only appears as an artifact of viewing things from a rotating--and thus noninertial--reference frame.

To answer your question directly: Sure. Imagine a ball tied to a string being swung in a horizontal circle. There is of course a "centripetal" force on the ball being provided by the string tension. If viewed from a rotating frame in which the ball is at rest, then you'd also have a centrifugal force acting on the ball. (Note that nothing actually pushes the ball outward.)

3. Oct 14, 2009

### daniel_i_l

Centrifugal force is an imaginary force that's felt by observers in a rotating frame.
The centripital force is the actual force that's causing the rotating movment. So a stationary observer in a rotating frame feels a centripital force towards the center of rotation and a centrifugal force in the opposite direction. The two cancel out which is why the observer is stationary in the rotating frame.

4. Oct 14, 2009

### jonjacson

¿do you mean that in the rotating frame you have both accelerations?

I don't agree with that , a stationary observer in a rotating frame doesn't feel a centripetal acceleration, he is at rest .

If the angular speed of the non inertial reference frame remains constant , these are the forces (in this non inertial frame):

-gravity

-normal, equal to the gravity force, so they cancel

- the friction force pushing inward at your feet

-the centrifugal pushing outward to your feet.

So the friction force is equal to the centrifugal (if you are at rest), and that means:

Friction force= mrw2 =centrifugal force

The net result is a=0, and as a consequence there is not centripetal acceleration.

¿do you agree?

---------------

It is very useful to make these problem:

A mass is at rest respect to the laboratory frame, while a frictionless turntable rotates beneath it . In the turntable frame ¿what are the forces?. And verify F=ma.

5. Oct 14, 2009

### Staff: Mentor

No. In the rotating frame the two forces (centripetal and centrifugal) cancel and the acceleration is zero.

Don't confuse centripetal acceleration with centripetal force. The centripetal force still exists in the rotating frame.

6. Oct 14, 2009

### jonjacson

I don't understand that, ¿can you show me the mathematical expression of the centripetal force in the non inercial frame?.

7. Oct 14, 2009

### Staff: Mentor

In the example I gave in post #2, the centripetal force--which equals mω²r--is provided by the string tension. That string tension exists regardless of the frame you use.

8. Oct 14, 2009

### jonjacson

Okey, now everithing is clear(I think), I was talking of another system, without a string, simply a mass above a rotating disk, so in that case the friction is the centripetal force ( because points to the center of rotation), and in the case of the string the tension is the centripetal force, in both cases centripetal acceleration is cero because centrifugal force is of the same magnitude and opposite sense ¿do you agree?

Other question when you use mw2r, that w is the angular speed of the rotation frame not of the object because is at rest, ¿am I wrong?.

Finally, in the turntable problem, you have that the body is not at rest, it has a speed v, so it appears a coriolis force pointing to the center of the rotating frame, so now that coriolis force is the centripetal force, we have the centrifugal force like always (if r is not parallel to the angular speed vector), and the net result of these two forces (coriolis pointing inward, and centrifugal pointing outward) is a centripetal acceleration mv2/r, the same as in the inertial frame.

¿everything is ok?

Last edited: Oct 14, 2009
9. Oct 14, 2009

### Staff: Mentor

Sounds good.

That's correct--ω is the rotational speed of the frame.

Right! In the turntable problem all forces are fictitious, since the centripetal acceleration itself is just an artifact of using a rotating frame.

10. Oct 14, 2009

### ruko

Centrifugal force is fictitious. It does not exist. A centrifuge should be called an inertiafuge. The question in my opinion should read, "Can centripetal force and inertia act together?"

11. Oct 14, 2009

### jonjacson

When I have seen your reply, I was happy because I had started to think that I understand this, but about the third point ¿did you mean centripetal or centrifugal?.

12. Oct 15, 2009

### Staff: Mentor

I meant centripetal--towards the center. As seen in the rotating frame, the mass execute circular motion and thus is centripetally accelerated. (I'm a bit confused by your question since you identified the acceleration as centripetal yourself in post #8.)

13. Oct 15, 2009

### Staff: Mentor

Fictitious inertial forces--such as coriolis and centrifugal--are extremely useful when analyzing motion from a rotating frame.

14. Oct 16, 2009

### monty37

my book has given the "stone tied to a string " case as an example of centrifugal force.
well,applying the same to engineering concepts ,a mass tied to a shaft undergoing rotary motion, the book says there is a centrifugal force acting ,but with respect to an observer outside there is also a centripetal force?so they need to balance each other out,right?

15. Oct 16, 2009

### Staff: Mentor

The shaft pulls the mass in a circle; the inward force it exerts can be called the centripetal force. Viewed from a rotating frame, you would have a fictitious centrifugal force acting outward on the mass. The two "forces" balance each other.

16. Oct 16, 2009

### jonjacson

Yes the acceleration is centripetal in the rotating frame , but i did not understand why you said at the end of your sentence "since the centripetal acceleration itself is just an artifact of using rotating frame".

Because I think that you use the concept of centripetal acceleration in the inertial frames too, so it is not something artificial developed to understand rotational frames (like coriolis or centrifugal force).

Perhaps I didn't express it sufficiently clearly.

17. Oct 16, 2009

### Staff: Mentor

All I meant was that when viewed from an inertial frame, the mass is not accelerating at all and no net force acts on it.

18. Oct 16, 2009

### monty37

that is what i thought,they balance out each other,but there is no mention of centripetal force in the book,it is being balanced differently.
can you apply the same balancing principle to planet rotation around the sun?

19. Oct 16, 2009

### Staff: Mentor

What book are you using? What force do they say balances the centrifugal force?
Sure, if you wanted to view it from a rotating frame in which the planet is at rest. (Not clear why you would want to do that, though.)

20. Oct 16, 2009

### D H

Staff Emeritus
Surely you meant a non-inertial frame, not an inertial frame. There is of course zero centrifugal force in an inertial frame.