Centrifugal force and angular velocity

In summary, the centrifugal force in a rotating reference frame is given by F = m*r*ω^2, where ω is the angular velocity and r is the distance to the center. This means that the larger the radius, the larger the centrifugal force. However, if the tangential velocity v is constant, then the farther out from the center, the smaller the centrifugal force. Angular velocity is the rate at which angle changes with respect to time, and can be calculated using revolutions per second or degrees per second. It is also related to the centrifugal force through the equation F = m*v^2/r. The centrifugal force is a fictitious force used in non-inertial reference frames, and can be
  • #1
Lsos
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According to the wikipedia page, when given an angular velocity, centrifugal force increases with radius. I always thought the larger the radius, the smaller the centrifugal force. I think I'm misunderstanding some term here (possibly "angular velocity"). Can someone please explain?
 
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  • #2
Angular velocity [itex]\omega[/itex] is the rate at which angle changes with respect to time (revolutions per second, degrees per second, radians per second, etc). If this rate is a constant, then the larger your distance to the center [itex]r[/itex] is, the larger the centrifugal force [itex]F[/itex] you will feel.

[itex]F = m \;r\;\omega^{2}[/itex]

However, if you are saying your tangential velocity [itex]v = r\;\omega[/itex] is constant, then the farther out from the center you are, the smaller the centrifugal force you experience, but this also means your angular velocity is smaller too.

[itex]F = m \frac{v^{2}}{r}[/itex]
 
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  • #3
Hi Lsos! :smile:
Lsos said:
… given an angular velocity, centrifugal force increases with radius.

Yes, if the angular velocity is fixed, the larger the radius, the more force you need to keep something in the circle.

Loosely speaking, changing the velocity from v to -v in the same time is obviously a larger acceleration if v is larger! :wink:
I always thought the larger the radius, the smaller the centrifugal force. I think I'm misunderstanding some term here (possibly "angular velocity"). Can someone please explain?

Angular velocity is angle per second.

It's equal to revolutions per second times 2π. :smile:
 
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  • #4
Hi,
The centrifugal force is a fictitious force used in non-inertial reference frames. In general, it is given by $$ F_{\text{centrifugal}} = m\textbf{w} \times (\textbf{w}\times\textbf{r}). $$ Here, ## \textbf{w} ## is the angular velocity of the rotating reference frame and ## \textbf{r} ## is the position of the particle relative to the rotating frame's origin.

Usually it will simplify to jfizzix' answer (the first equation).

From a more qualitative perspective, imagine a large disc spinning. If you stand near the centre, you move in a small circle but not very fast. As you move out, you move faster and faster and you will find it more difficult to stay on the disc.

:)

PS: I used ##\textbf{w}## because for some reason the TeX code for omega isn't working... :\
 
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quarkgazer said:
PS: I used ##\textbf{w}## because for some reason the TeX code for omega isn't working... :\
I think your use of the bold face text is the problem. Latex assumes what follows is text. You can use vectors like this$$ F_{centrifugal} = m\vec{\omega} \times (\vec{\omega} \times \vec{r}) $$

AM
 
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  • #6
Ok...yeah. I think I get it. Seems like a very simple concept, but I just need to wrap my aging mind around this. Thanks everyone!
 

FAQ: Centrifugal force and angular velocity

What is centrifugal force?

Centrifugal force is an apparent force that appears to act on an object moving in a circular path. It is a result of the object's inertia, or tendency to continue moving in a straight line, combined with the curvature of its circular path.

How is centrifugal force related to angular velocity?

Centrifugal force is directly proportional to the square of the object's angular velocity. This means that as the object's angular velocity increases, so does the magnitude of the centrifugal force acting on it.

Can centrifugal force be greater than the force of gravity?

Yes, in some cases, centrifugal force can be greater than the force of gravity. This occurs when an object is spinning at a high enough speed and the centrifugal force acts in the opposite direction of gravity, causing the object to feel weightless.

How does angular velocity affect centrifugal force?

As mentioned earlier, the magnitude of centrifugal force is directly proportional to angular velocity. This means that as the angular velocity of an object increases, the centrifugal force acting on it also increases.

What is the difference between centrifugal force and centripetal force?

Centrifugal force is an apparent force that appears to act on an object moving in a circular path, while centripetal force is a real force that actually acts on the object and keeps it moving in a circular path. Centrifugal force acts away from the center of the circle, while centripetal force acts towards the center of the circle.

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