# Centrifugal and inertial force in centrifuge

• member 731016
In summary: William McCall. The centrifuge tube is labeled "Inertial force" because it is a force that appears in a rotating frame, but not in an inertial frame.
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Homework Statement
Would anybody please know why in my textbook below they show the centrifugal force with a inertial force? I though the centrifugal force was a result of the particle's inertia when viewed from an inertial frame. I don't understand why the diagram shows an inertial force when there was no previous mention of it in the textbook.

Many thanks!
Relevant Equations
## F_c = \frac {mv^2}{r} ## is a real force from an inertial frame.

An inertial force is a force that appears in a non-inertial frame but not in an inertial frame. The centrifugal force is an example of an inertial force. Also, ##\frac{mv^2}{r}## is not a force in an inertial frame; it is mass × acceleration. It appearss the centrifugal force in a rotating frame. I don't understand the label "Inertial force" next to the centrifuge tube on the right.

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kuruman said:
An inertial force is a force that appears in a non-inertial frame but not in an inertial frame. The centrifugal force is an example of an inertial force. Also, ##\frac{mv^2}{r}## is not a force in an inertial frame; it is mass × acceleration. It appearss the centrifugal force in a rotating frame. I don't understand the label "Inertial force" next to the centrifuge tube on the right.
Thank you for your help @kuruman ! Sorry what did you mean by
##\frac{mv^2}{r}## is not a force in an inertial frame; it is mass × acceleration.
?

I though ##\frac {mv^2}{r} ## is a force in an inertial frame since ##a_c = \frac {v^2}{r}## so ##F_c = ma_c##. Did you mean the centripetal force is not a force in a non-inertial frame?

Many thanks!

kuruman said:
##\frac{mv^2}{r}## is not a force in an inertial frame;
It is an identifiable force, but it is not a specific applied force. The centripetal force is that component of the net force which is normal to the velocity.

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haruspex said:
It is an identifiable force, but it is not a specific applied force.
For a mass rotating at the end of a taut string, ##F_{net}=ma## translates to ##T=\frac{mv^2}{r}##. The net force is on the LHS and mass times acceleration on the RHS. I see no benefit in thinking of the RHS as a force but I see harm in the confusion it might cause in the minds of students who are learning how to construct and interpret FBDs.

member 731016
What book is this? That arrow labeled ac does not make sense either. The plane of the circular trajectory is horizontal so the centripetal acceleration is horizontal. And so is the (inertial) centrifugal force.
And the tube is vertical when the centrifuge is not spinning so there is actually no centripetal acceleration or inertial force.

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nasu said:
What book is this? That arrow labeled ac does not make sense either. The plane of the circular trajectory is horizontal so the centripetal acceleration is horizontal. And so is the (inertial) centrifugal force.
And the tube is vertical when the centrifuge is not spinning so there is actually no centripetal acceleration or inertial force.
Thank you for your replies @haruspex , @kuruman and @nasu !

It is University Physics Volume 1 (Openstax)

## What is the difference between centrifugal and inertial force in a centrifuge?

Centrifugal force is a perceived force that acts outward on a mass when it is rotated around a center. It is often described as a "fictitious" or "pseudo" force because it arises from the inertia of the mass moving in a circular path. Inertial force, in the context of a centrifuge, refers to the resistance of the mass to the change in its state of motion. While centrifugal force is experienced in the rotating frame of reference, inertial force is experienced in the inertial frame of reference.

## How does centrifugal force work in a centrifuge?

In a centrifuge, when a sample is spun at high speeds, the particles in the sample experience a force that pushes them outward, away from the axis of rotation. This outward force is the centrifugal force, which is a result of the inertia of the particles trying to move in a straight line while being forced into a circular path by the rotating container. This force causes denser particles to move outward more quickly than less dense particles, facilitating their separation.

## Why is centrifugal force called a "fictitious" force?

Centrifugal force is called a "fictitious" or "pseudo" force because it does not arise from any physical interaction but rather from the inertia of an object in a rotating reference frame. It is an apparent force that is observed only in a non-inertial (rotating) frame of reference. In an inertial frame of reference, the effects attributed to centrifugal force are explained by the object's tendency to move in a straight line due to its inertia.

## What role does inertial force play in the operation of a centrifuge?

Inertial force in a centrifuge refers to the resistance of particles to changes in their motion. When the centrifuge begins to spin, the particles initially resist the change in motion due to their inertia. As the speed increases, this resistance is overcome, and the particles start to move outward due to the centrifugal force. Inertial force is crucial in understanding the initial behavior of particles when the centrifuge starts and stops, as well as in the distribution of particles within the spinning sample.

## How do centrifugal and inertial forces affect the separation process in a centrifuge?

In a centrifuge, centrifugal force causes particles to move outward, with denser particles moving more quickly and settling faster than less dense particles. Inertial force, on the other hand, affects how particles initially respond to the spinning motion and how they distribute themselves within the sample. The balance between these forces determines the efficiency and effectiveness of the separation process. Properly calibrated centrifuges use these forces to achieve optimal separation based on particle density and size.

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