In the case of my animation
https://www.geogebra.org/m/mjnqb8vk
before the collision, the inertia of the mass m1 is not a vector in
the reference of m1 but it is certainly a vector in the reference of
the mass m2 because it moves horizontally to the right.
And the inertia of mass m2 is certainly a vector in the reference of
m1 because it moves horizontally to the left.
It's correct?
Luigi Fortunati
In the case of my animation https://www.geogebra.org/m/mjnqb8vk before the collision, the inertia of the mass m1 is not a vector in
the reference of m1 but it is certainly a vector in the reference of
the mass m2 because it moves horizontally to the right.
And the inertia of mass m2 is certainly a vector in the reference of
m1 because it moves horizontally to the left.
It's correct?
Inertia is a property of an object, not a dynamic variable. I think
what you mean is momentum. Momentum is part of a Lorentz invariant
4-vector:
p = {energy/c, x-momentum, y-momentum, z-momentum} (in momentum units)
The momentum parts comprise a vector in 3-space. This energy-momentum 4-vector is conserved in any collision:
p(m1 before) + p(m2 before) = p(m1 after) + p(m2 after)
This is true even for inelastic collisions as long as the energy lost to friction/deformation is included in the the after energy components. This
is true relativistically provided the relativistically correct energy and momenta are calculated.
Inertia is a property of an object...
Richard Livingston il 24/10/2023 18:21:13 ha scritto:
Yes, that's right, inertia is that property of bodies that makes them
go straight at uniform speed.
Yes, that's right, inertia is that property of bodies that makes them
go straight at uniform speed.
No, inertia is the ability of a body to resist being accelerated. Its quantity is what we think of as inertial mass. It is a scalar.
No, inertia is the ability of a body to resist being accelerated.=20
George Hrabovsky il 26/10/2023 11:12:16 ha scritto:
Yes, that's right, inertia is that property of bodies that makesNo, inertia is the ability of a body to resist being accelerated.
them go straight at uniform speed.
Its quantity is what we think of as inertial mass. It is a scalar.
If inertia is the ability of bodies to resist acceleration (which is
a vector), then it cannot be a scalar!
George Hrabovsky il 26/10/2023 11:12:16 ha scritto:
No, inertia is the ability of a body to resist being accelerated.
Inertia is (first of all) a property of bodies and, therefore, every
material body always has this property, at any moment, both before,
during and after the collision (there are no bodies that have inertia
at certain moments and in others don't have it).
Instead, resistance to acceleration is not always there, it is only
there when acceleration occurs, because the two things are connected.
There is resistance to acceleration if there is acceleration and there
is no resistance to acceleration if there is no acceleration.
Inertia in the absence of any acceleration (which must not resist acceleration) is a completely different thing from inertia in the
presence of acceleration (which must resist acceleration).
You can understand everything by looking at my animation https://www.geogebra.org/m/mjnqb8vk
George Hrabovsky il 26/10/2023 11:12:16 ha scritto:This is wrong. If you multiply a vector by the scalar 1/2, then each component is half of what it was; you have resisted the vector by using a scalar.
If inertia is the ability of bodies to resist acceleration (which is a vector), then it cannot be a scalar!Yes, that's right, inertia is that property of bodies that makes them
go straight at uniform speed.
No, inertia is the ability of a body to resist being accelerated. Its
quantity is what we think of as inertial mass. It is a scalar.
On 10/28/23 1:02 PM, Luigi Fortunati wrote:
George Hrabovsky il 26/10/2023 11:12:16 ha scritto:force is impressed on the object.
Yes, that's right, inertia is that property of bodies that makesNo, inertia is the ability of a body to resist being accelerated.
them go straight at uniform speed.
Its quantity is what we think of as inertial mass. It is a scalar. Actually, inertia does both -- it resists acceleration when a force is applied, and it makes an object move in a uniform straight line when no
If inertia is the ability of bodies to resist acceleration (which is
a vector), then it cannot be a scalar!
No.
When a force is impressed upon a massive object, the object's
inertia resists in the opposite direction.
So inertial CANNOT be a vector if it is to act the same for
all forces in all directions.
Indeed "inertia" is really another name for "mass",
which is clearly a scalar.
Inertia is a consequence of conservation of energy. Consider the
following argument:
-A particle of mass m_0 at rest has zero momentum and energy
E=m_0 c^2
-Quantum mechanically the wave function has frequency
\omega_0 = \frac{m_0 c^2}{\hbar}, and k=0.
-If you Lorentz transform to a moving frame with velocity beta,
the frequency becomes
\omega_1 = \omega_0 \gamma
and the wavenumber becomes
k = \omega_0 \gamma \beta
In other words, to promote an object at rest in one frame to
being at rest in a moving frame, you have to add energy. This
is the experienced as "inertia", the tendency for objects to
remain in constant motion unless disturbed. (By disturbed,
I mean energy is added or subtracted from the object.)
All this concerns the inertia of a single mass that moves without having to deal with the inertia of another mass with which it collides.
When in my animation
https://www.geogebra.org/m/mjnqb8vk
body m2 is suddenly hit by m1, does its inertia passively accept the intrusion or does it rebel and opposes in the opposite direction?
[[Mod. note -- The problem with phrases like "passively accept" or
"rebel" or "oppose" is that it's hard to pin down their meanings.
For example, how should we operationally define "passive acceptance"?
Without a clear operational definition, it's hard to do a careful
analysis.
Newton's 2nd law is unambiguous: apply a (vector) net force F to
an object, and the object accelerates with a (vector) acceleration.
The acceleration vector is observed to be proportional to the net-force vector, with a fixed proportionality constant (which we call the
"inertial mass", or just "mass" for short) for any given object.
Each of these phrases has a clear operational definition.
-- jt]]
Newton says: <L The vis insita, or innate force of matter, [...]
Newton says: <L The vis insita, or innate force of matter, [...]
The translator used a PUN on the word "force".
In Newtonian mechanics, force is a vector while the "vis insita" is a scalar, which today is called mass.
Instead, resistance to acceleration is not always there, it is only there when acceleration occurs, because the two things are connected.
This is in error. Forces acting on a body accelerate the mass of the body.
The mass is always there, and it is a measure of inertia. This is encapsulated in Newton's second law, F = m a, F is the applied force, m is the mass, and a is the acceleration. F and a are vectors, m is a scalar.
There is resistance to acceleration if there is acceleration and there is no resistance to acceleration if there is no acceleration.
The mass is always there, otherwise how would the body know when to have mass or not?
Inertia in the absence of any acceleration (which must not resist acceleration) is a completely different thing from inertia in the presence of acceleration (which must resist acceleration).
Why?
You can understand everything by looking at my animation https://www.geogebra.org/m/mjnqb8vk
Your animation demonstrates the conservation of momentum and the effects of friction (a force caused by electromagnetism), so it has nothing to do with inertia intrinsically.
Certainly, but the forces that act on a body also have another consequence: they activate the body's resistance force!
And vice versa, the body's (inertial) resistance force is activated *only* when the external force intervenes.
Newton also says it: "A body exerts this force only, when another force, impressed upon it, endeavors to change its condition; and the exercise of this force may be considered both as resistance and impulse; it is resistance, in so far as the body, formaintaining its present state, withstands the force impressed; it is impulse, in so far as the body, by not easily giving way to the impressed force of another, endeavors, to change the state of that another. Resistance is usually ascribed to bodies at
You can understand this by looking at my animation where the bodies m1 and m2 (before the collision) do not have to resist anything because no one is accelerating them and, instead, during the collision they both have to resist because they areaccelerating each other.
My animation demonstrates that there is a simultaneity between inertia and electromagnetic forces.
In fact, the electromagnetic forces are activated only during the collision, that is, precisely at the moment in which both bodies m1 and m2 need a force to be able to resist the mutual external acceleration.
This means that it is precisely the bodies m1 and m2 that use *their* electromagnetic forces (what else if not?) to be able to oppose each other.
In fact, in the lower part of my animation (despite there being contact between m1 and m2) no electromagnetic force is activated because the inertias do not activate them (not needing them).
Newton also says it: "A body exerts this force only, when another force,
impressed upon it, endeavors to change its condition; and the exercise of
this force may be considered both as resistance and impulse; it is
resistance, in so far as the body, for maintaining its present state,
withstands the force impressed; it is impulse, in so far as the body, by not >> easily giving way to the impressed force of another, endeavors, to change
the state of that another. Resistance is usually ascribed to bodies at rest, >> and impulse to those in motion; but motion and rest, as commonly conceived, >> are only relatively distinguished; nor are these bodies always truly at
rest, which commonly are taken to be so."
You suggest that inertia is a force.
[...]
Tom Roberts il 10/12/2023 11:52:28 ha scritto:
On 10/23/23 6:31 AM, Luigi Fortunati wrote:
[...]
[The context of this question is clearly Newtonian mechanics.
But my answer holds for relativistic mechanics as well.]
To definitively answer the question "is inertia a vector", one must find
"inertia" in some equation(s). Unfortunately, "inertia" does not appear
in any equation of mechanics. So the question is meaningless, or at
least unanswerable.
[This includes Newton's original "vis insita".]
Note: do not be confused by "moment of inertia" -- look at its
definition and you'll see it is misnamed, and is really the second
moment of mass.
In modern physics,the closest quantity to "inertia" is mass, which is
clearly a scalar (i.e. not a vector).
Tom Roberts
What is mass for you?
If for you mass is just a quantity of matter, you are right: it is a
scalar, because it has no direction.
Instead, if the mass is an inertial body or a body that reacts, it has direction.
In fact, the inertial body moves with uniform rectilinear motion (and
the motion is a vector) and the body that reacts exerts an opposing
force (and the force is a vector).
This is why inertia is a vector: because it moves in only one direction
or reacts in only one direction.
Luigi Fortunati
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