Fake forces on rotating frames of reference.

In summary, a rotating observer on a frictionless disk sees a ball on the edge following a circular path with an angular velocity ω opposite of his frame of reference. This movement is explained by introducing non-Newtonian forces due to being in a non-inertial frame. The ball experiences both centrifugal and Coriolis forces, which result in an inwards centripetal force that matches the circular motion. The disk itself is not moving in the inertial frame.
  • #1
House
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Suppose we have a rotating frictionless disk and there is a rotating observer on the center of it. Furthermore, suppose a very small ball on the disk's edge. Now we clearly know that the ball is not moving but the rotating observer sees the ball following a circular path with an angular velocity ω opposite of the one of his frame of reference. He now has to explain that movement and, since he is in a non-inertial frame, he has to introduce some non Newtonian forces. Accepting that the ball has a relative velocity vr in the non-inertial frame, the question is:
Is there a centifugal force and a Coriolis force acting on the ball? Or does the ball have to "physically" be included on the disk?
 
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  • #2
Update: The math says that the rotating observer measures a force given by: F = mω×(ω×r) which is towards the center of the circular motion. Is that it?
 
  • #3
House said:
Now we clearly know that the disk is not moving...
I assume you mean the ball is at rest in the inertial frame of reference.

House said:
Accepting that the ball has a relative velocity vr in the non-inertial frame, the question is: Is there a centifugal force and a Coriolis force acting on the ball?
Yes, both are acting in opposite directions, and their net effect is the inwards centripetal force, that matches the circular movement in the rotating frame.
 
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1. What are fake forces on rotating frames of reference?

Fake forces, also known as inertial forces, are apparent forces that arise in rotating frames of reference. These forces are not true forces, but rather the result of the frame of reference itself being in a state of acceleration or rotation.

2. How do fake forces affect objects in a rotating frame of reference?

Fake forces do not actually affect objects in a rotating frame of reference. Instead, they are perceived to exist due to the frame of reference itself being in motion. Objects in a rotating frame of reference will continue to move in a straight line, unless acted upon by a true force.

3. What are some examples of fake forces on rotating frames of reference?

Some common examples of fake forces include centrifugal force, Coriolis force, and Euler force. Centrifugal force is the apparent force that causes objects to move away from the center of rotation. Coriolis force is the apparent force that causes objects to appear to veer to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. Euler force is the apparent force that causes objects to move in a circular path when viewed from a rotating frame of reference.

4. How can we distinguish between fake forces and true forces?

One way to distinguish between fake forces and true forces is to consider the frame of reference in which the forces are observed. If the frame of reference is accelerating or rotating, then any perceived forces are fake, while if the frame of reference is inertial, then the forces are considered to be true.

5. Are fake forces important in understanding motion and dynamics?

Yes, understanding fake forces is crucial in accurately describing and predicting the motion of objects in rotating frames of reference. Without accounting for these forces, our understanding of dynamics would be incomplete and could lead to incorrect conclusions about the behavior of objects in these frames of reference.

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