Can Fictitious Force Become Real ?

[Antonio Lao]

Can Fictitious Force Become Real ?

Centrifugal force is considered as a fictitious force. For an object of $m$ mass, it is given by

$$F_{centrifugal} = - m \vec{a}_{centripetal} = \frac{mv^2}{r} \hat{r}$$

The fictitiousness comes from the use of a noninertial rotating coordinate system for measuring coordinates. But if the rotating coordinate system is removed would this removal also cause the force to become real?

 

[Olias]

I believe the force manifests itself to a 'Directional' linear force at the moment rotation is removed?..the Newtonian Gravitational Law transpires to the tangient?

 

[Antonio Lao]

I believe the force manifests itself to a 'Directional' linear force at the moment rotation is removed?..the Newtonian Gravitational Law transpires to the tangient?

Thanks. In other words, removing coordinate system changed the 'direction' of the system?

 

[zefram_c]

I am not sure what you mean by "removing the coordinate system"; can you explain?
To someone in an inertial frame, the fictitios forces observed by someone thinking himself at rest in an accelerating frame look like a manifestation of the Law of Inertia. See for example http://www.infoplease.com/ce6/sci/A0811114.html or http://hyperphysics.phy-astr.gsu.edu/hbase/corf.html for how this applies to the centrifugal force. I don't think anyone, whether in an inertial frame or not, would ever see a fictious force becoming 'real'; after all, if there is an agent causing the force in one frame, that agent will have to be present in all other frames.

 

[Antonio Lao]

I am not sure what you mean by "removing the coordinate system"; can you explain?

By removing the coordinate system is the same as removing the mass although the mass can still be canceled out from the following.

$$F = ma = \frac{mv^2}{r}$$

$$a = \frac{v^2}{r}$$

$$ar = v^2$$

as the velocity approaches the speed of light in vacuum, all noninertial coordinates vanish and the inner product of acceleration and a distance become a constant, the square of light speed in vacuum.

$$\vec{a} \cdot \vec{r} = c^2$$

The acceleration $a$ is a generalized term. This can account for fictitious centrifugal acceleration as real outward spiral repulsive force of antigravity and also defines a new kind of mass as kinetic mass, a repulsive mass for antigravity.

Furthermore, we can hypothesize that the centipetal acceleration is inversely proportional to the centrifugal acceleration.

$$a_{centripetal} = \frac{k}{a_{centrifugal}}$$

where $k$ is the constant of proportionality. This $k$ is intimately related to the mass, inertia or gravitational or the new kinetic mass.

$$k = \frac{F_E}{m_E} \cdot \frac{F_B}{m_B}$$

Similar to temperature, $k$ is a dynamic constant.

 

[pallidin]

Thanks. In other words, removing coordinate system changed the 'direction' of the system?

I'm not so sure it "changed" the direction of the system, since the expressed vector was held in potential all along. It simply became expressed as the system translated from one state to another.

Also, I would caution against manipulating dependent mathematical terms to the effort of "cancellation" Many mathematical equations are written to describe a valued dependency, such as f=ma.
This dependency often(though not always) requires that a value be ascribed to each term. If one cancels mass, then f=a, which makes the equation non-sensical. Rather than cancelling mass, the value should be set as zero. As such, f=0xA, which makes more sense.
In other words, one cannot "exclude" the mass term from a mathematical expression that is dependent on it. It must be given a value, even if that value is zero.
In other words, algebraic manipulation in some equations may well reflect the abilities of that manipulation, but may yet have no true basis in reality.
Perhaps put another way, let's say that a=bc. With respect to using numbers, this equation is correct, and with certain extensions "b" can be cancelled. However, f=ma is NOT strictly a numerical equation. It is a "concept-dependent" equation, and follows different rules.
Let's consider another example.
Take the standard simple formula used in electronics, p=ie, which means power equals current times voltage. This is a dependency relationship.
You can have voltage without current, but you cannot have current without voltage. Agreed?
If you "cancel" voltage from the equation through extension the entire equation collapses, because it invalidates the other term, current. So, since current cannot exist without voltage, voltage is never "cancelled" It's value might be zero, but the term itself is not canceled from equation CONSIDERATION. Get it?
Similarly, mass can exist without acceleration, but acceleration cannot exist without mass. Therefore, any equation which uses acceleration in it's term CANNOT have mass "cancelled", only it's value set to zero.

 

[Antonio Lao]

pallidin,

At first, I thought of assigning all mass values to 1 instead of cancellation. The number 0 can be the same as the ratio of 1 over infinity. But the ratio of 1 over 1 is 1 which to me means that two distinct phenomena are in equilibrium and the proportionality constant is also 1.

If we investigate all the proportionality constants of nature as found in all equations of the physical sciences, it is rarely equal exactly 1. Is there a deeper hidden asymmetry behind them? One we can never understand?

Why are we always comparing between the small and the large, between the slow and the fast, between the weak and the strong, between the near and the far? Why can things be all equal by comparison? Because if they are equal then there is no effect of motion, of force, of weight, of color, of pattern, of contrast - a state of perfect symmetry such as the vacuum.