Understanding the centrifugal force

In summary, the centrifugal force is defined as Fcf = m(Ω×r)×Ω, where Ω×r is the instantaneous velocity at a point on the outside of a circle (or other rotating path) and Ω is the angular velocity. It is responsible for the outward radial direction of objects in circular motion and is observed in noninertial frames, but not in inertial frames.
  • #1
cytochrome
166
3
I'm learning about mechanics in noninertial frames and I'd like to clarify the apparent centrifugal force.

To set things straight,

Centrifugal force = Fcf = m(Ω×rΩ

where Ω×r is the instaneous velocity at a point on the outside of a circle (or other rotating path) and Ω is the angular velocity?

By looking at a picture, this would have the centrifugal force pointing out radially from the rotating path (which makes sense when imagining a centrifuge for example).

Is this force called "fictitious" because there is actually no force (as observed from a rotating frame of reference, or an inertial frame?) that is causing an object to accelerate in this radial direction? What is the force exactly?

For example - Imagine you are spinning a ball on a string around in circles and the string breaks, causing the ball to fly outward perpandicular to the direction of motion. Is the centrifugal force responsible for this?

How does this force relate to observations seen from a noninterial or inertial frame?
 
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  • #2
In inertial frame.

There is no centrifugal force. The reason the string is under tension is because it pulls on the object in order to keep it centripetally accelerating to travel in a circular path. The reason the object flies away when the string breaks is because it continues to travel in the straight path.

In a rotating frame. (Frame rotation matches rotation of the object.)

Object is stationary. It's not moving at all. So the only explanation for the tension in the string is gravity-like force pulling on the object, forcing it away from center. That's the centrifugal force. When the string snaps, that force accelerates the object away from center.The centrifugal force is a fictitious force because it does not exist in an inertial frame of reference. It only manifests when we try to use Newton's Laws to describe motion in an accelerated frame of reference.
 

Related to Understanding the centrifugal force

1. What is centrifugal force?

Centrifugal force is the apparent outward force that appears to act on an object moving in a circular path. It is caused by the inertia of the object trying to continue in a straight line while being forced to move in a curved path.

2. How is centrifugal force different from centripetal force?

Centrifugal force is often confused with centripetal force, but they are actually two different forces. Centripetal force is the force that pulls an object towards the center of a circular path, while centrifugal force is the opposite, pushing the object away from the center.

3. What is the role of centrifugal force in a centrifuge?

In a centrifuge, centrifugal force plays a crucial role in separating substances of different densities. The spinning motion of the centrifuge causes the heavier substances to move towards the outer edges while the lighter substances stay towards the center, allowing for separation.

4. How does centrifugal force affect objects of different masses?

Centrifugal force is proportional to an object's mass and its distance from the center of rotation. This means that objects with greater mass or placed at a greater distance from the center will experience a stronger centrifugal force.

5. Can centrifugal force be felt by humans?

No, centrifugal force is not a real force but rather an apparent force due to an object's inertia. It is not a physical force that can be felt, but rather a perceived force that explains the motion of objects in circular paths.

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