Can we model fictitious forces using vectors?

[flyingpig]

Homework Statement

Let's say that you are on a Ferris Wheel or you are spinning a Yo-yo horizontally in a circle. There is a fictitous force known as centrifuge force that is pushing the car or yo-yo outwards.
However, the centripetal force that is keeping it in tact, is a vector pointing towards the center. We know that F [tex]\alpha[/tex] a, so even though centrifuge is a fictitious force, how come the "vector" of it is opposite to that of centripetal acceleration?

The Attempt at a Solution

I have been pondering this question for 3 days...

For the yoyo case, would to be just the tension?

T = [tex]\stackrel{mv²}{r}[/tex]

Also, I read a proof on how centripetal acceleration is derived, but why do we always neglect the negative sign in the formula a = [tex]\stackrel{-|v²|}{r}[/tex]

 

[D H]

Ignoring the rotation of the Earth itself you are an inertial observer when you look at a spinning yo-yo. There is no need to invoke a centrifugal force in this case. There is no centrifugal force in this case.

Centrifugal force are needed to force-fit Newton's laws to the domain of rotating reference frames (a domain in which Newton's laws do not truly apply).

 

[flyingpig]

Ignoring the rotation of the Earth itself you are an inertial observer when you look at a spinning yo-yo. There is no need to invoke a centrifugal force in this case. There is no centrifugal force in this case.

Centrifugal force are needed to force-fit Newton's laws to the domain of rotating reference frames (a domain in which Newton's laws do not truly apply).

Ferris Wheel case?

 

[flyingpig]

So I still don't get it...

 

[rwisz]

?

I can provide a response to this question by explaining the concept of fictitious forces and their relationship with vectors.

Fictitious forces are forces that appear to act on an object in a non-inertial reference frame, but are actually due to the acceleration of the reference frame itself. In the case of a Ferris Wheel or a yo-yo, the object is moving in a circular motion and therefore experiencing a centripetal acceleration towards the center.

The centrifugal force, also known as the centrifuge force, is a fictitious force that appears to push the object away from the center of the circular motion. This force is not a real force, but rather a perceived force due to the object's inertia wanting to continue moving in a straight line while the reference frame is accelerating towards the center.

Now, in terms of vectors, we know that forces are vectors and therefore have both magnitude and direction. The direction of a force is determined by its effect on the motion of an object. In the case of the centrifugal force, it appears to push the object away from the center, which is in the opposite direction of the centripetal acceleration. This is why the vectors for these two forces are opposite to each other.

As for the formula for centripetal acceleration, the negative sign is often neglected because it is already implied in the direction of the vector. The magnitude of the centripetal acceleration is always positive, and the direction is determined by the direction of the velocity vector. Therefore, the negative sign is not necessary to include in the formula.

In conclusion, we can model fictitious forces using vectors by understanding their relationship to the acceleration of the reference frame and the direction of their effects on the motion of an object. The negative sign in the formula for centripetal acceleration is often neglected because it is already implied in the direction of the vector.