The simulation is this: https://www.geogebra.org/m/tnas7mbn
When we start the rotation with the "Start", *pairs* of opposing
forces are activated: the rope exerts its centripetal force on the
ball (otherwise the ball would not rotate) and the ball exerts its centrifugal force on the rope (otherwise the tension of the rope
would not exist).
Is there (somewhere in my simulation) a centripetal force lacking
its corresponding centrifugal force?
Is there (somewhere in my simulation) a preponderance of centripetal
over centrifugal forces?
On 12/14/22 2:52 PM, Luigi Fortunati wrote:
The simulation is this: https://www.geogebra.org/m/tnas7mbn
When we start the rotation with the "Start", *pairs* of opposing
forces are activated: the rope exerts its centripetal force on the
ball (otherwise the ball would not rotate) and the ball exerts its
centrifugal force on the rope (otherwise the tension of the rope
would not exist).
This is wrong.
Your diagram shows the system in the inertial frame of
the center. In this frame there is no "centrifugal force".
The tension in the rope exerts a centripetal force on the ball,
causing it go move in a circle.
https://www.geogebra.org/m/tnas7mbnI have highlighted, coloring them in red, some centrifugal forces.
In my simulation
https://www.geogebra.org/m/tnas7mbnI have highlighted, coloring them in red, some centrifugal forces.
These forces exist because they are the reaction to the corresponding centripetal forces (third principle).
These forces are centrifugal because they point in the opposite direction to the corresponding centripetal forces.
Every centripetal force has its corresponding centrifugal force (and vice versa).
I'm not discussing outlandish or far-fetched theories but pure Newtonian physics.
And, as I said, if there are any errors in my simulation, I'm ready to make whatever corrections are necessary.
So why is nobody willing to clarify the matter? Why so much reticence?
On 23/12/2022 08:24, Luigi Fortunati wrote:<snip>
The equations of motion of Newtonian mechanics for point particles with constant mass are always defined with reference to an inertial frame of reference, and you get the equations describing these Newtonian within a non-inertial reference frame simply by writing the coordinates of the
point particles wrt. an inertial frame in terms of coordinates referring
to a non-inertial frame.
This leads to additional terms when taking the time derivatives.
3. From a Newtonian-dynamics-in-an-inertial-reference-frame perspective,
if I jump on (and hold on to) a merry-go-round, I don't feel a
centrifugal force. Rather, the merry-go-round exerts a *centripetal*
force on me, accelerating me inwards (so that I move in a circle around
the rotation axis). The *centripetal* acceleration is what I feel.
On Friday, 23 December 2022 at 16:09:41 UTC+1, Hendrik van Hees wrote:
On 23/12/2022 08:24, Luigi Fortunati wrote:<snip>
The equations of motion of Newtonian mechanics for point particles with
constant mass are always defined with reference to an inertial frame of
reference, and you get the equations describing these Newtonian within a
non-inertial reference frame simply by writing the coordinates of the
point particles wrt. an inertial frame in terms of coordinates referring
to a non-inertial frame.
This leads to additional terms when taking the time derivatives.
Please correct me if I am mistaken, but F=ma is not only valid in inertial frames, is it? Indeed, I find the way you are presenting things here still risks to give the impression that these "fictitious", aka "apparent" forces are only an artefact of the algebra, while in that sense they are rather a misnomer for the quite real forces an observer in that non-inertial frame would feel and measure. Put simply, if one jumps on a merry-go-round, fighting the centrifugal force is a real and properly physical thing, no?
Julio
[[Mod. note --
1. Just to be clear: the quoted text was written by Hendrik van Hees,
not by Luigi Fortunati.
2. I agree with Hendrik: F=ma (with F only including "real" forces) is only
valid in an inertial reference frame. To do Newtonian dynamics in a
non-inertial reference frame, one must augment F to also include
fictitious forces (such as the Coriolis force).
3. From a Newtonian-dynamics-in-an-inertial-reference-frame perspective,
if I jump on (and hold on to) a merry-go-round, I don't feel a
centrifugal force. Rather, the merry-go-round exerts a *centripetal*
force on me, accelerating me inwards (so that I move in a circle around
the rotation axis). The *centripetal* acceleration is what I feel.
-- jt]]
Sysop: | Keyop |
---|---|
Location: | Huddersfield, West Yorkshire, UK |
Users: | 343 |
Nodes: | 16 (4 / 12) |
Uptime: | 29:05:56 |
Calls: | 7,515 |
Calls today: | 12 |
Files: | 12,713 |
Messages: | 5,642,040 |
Posted today: | 2 |