From: Ka-In Yen on

Danny Dot wrote:
> --
> Danny Dot
> Look at my site and see how NASA treats a creative mind!!!
> The summary is "Not Very Well" :-)
> www.mobbinggonemad.org
>
>
> "Ka-In Yen" <yenkain(a)yahoo.com.tw> wrote in message
> news:1156469606.545703.194940(a)i42g2000cwa.googlegroups.com...
> >
> > Home work for Eric Gisse:
> > A rectangle sits in 3D space. The area vector of the rectangle is A,
> > and the legth vector of one side of the rectangle is L. Please find
> > the length vector of the other side of the rectangle?
> >
>
> I have always thought of mass as a scalar, not a vector. Momentum is a
> vector, but not mass. Maybe I am wrong.
>
Dear Danny Dot,

Thank you for your comment. You are right; mass is scalar.
In three dimensional vector algebra, linear mass density and
surface mass density are vectors; shortly I call them mass
vector.


The proof of mass vector.

Ka-In Yen
yenkain(a)yahoo.com.tw
http://www.geocities.com/redlorikee


Introduction:
In this paper, we will prove that linear mass density and
surface mass density are vector, and the application of mass
vector is presented.


1. The unit of vector.


In physics, The unit of three-dimensional cartesian coordinate
systems is meter. In this paper, a point of 3-D coordinate
system is written as


(p1,p2,p3) m, or (p:3) m


and a vector is written as


<a,b,c> m, or <a:3> m


or


l m<i,j,k> = <a,b,c> m


where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
and <i,j,k> is a unit vector which gives the direction of
the vector.


For three reasons, a magnitude of a vector can not add to a
scalar:
i) The magnitude belongs to the set of vector; it's a
portion of a vector. Scalar belongs to a field.
ii) The magnitude is real non-negative number, but scalar
is real number.
iii) The unit of magnitude is meter, but scalar has no unit.
This is a major difference between physics and mathematics.
5m+3 is meaningless.


2. Linear mass density is a vector.


The mass of a string is M kg, and the length of the string
is l m<i:3>. Where l m is the magnitude of the length, and
<i:3> is a 3-D unit vector which gives the direction of the
string. Then the linear mass density of the string is:


M/(l<i:3>)=(M/l) (kg/m)<i:3>


The direction, <i:3>, is not changed by "division", so we
can move <i:3> from denominator to numerator. A direction
is changed by -1 only. A proof is found in Clifford algebras:


[Proof]
k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
=(k/l) <i,j,k>
where l is the magnitude of <a,b,c>, and <i,j,k> is the
unit vector of <a,b,c>.
[Proof]


3. Surface mass density is a vector.


A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
and <j:3> are unit vectors. The area vector of the parallelogram
is the cross product of these two vectors.


l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
= lh abs(sin(theta)) (m^2)<k:3>


Where theta is the angle between <i:3> and <j:3>. <k:3> is
a unit vector which is perpendicular to <i:3> and <j:3>.
For AXB=-BXA, an area has two directions.


We can divide the area vector by the length vector.


lh*abs(sin(theta))<k:3>/[l<i:3>]
=h<i:3>X<j:3>/<i:3>
=h(<i:3>X<j:3>)X<i:3>
(The direction, <i:3>, is not changed by "division", and
the division is replaced by a cross product.)
=-h<i:3>X(<i:3>X<j:3>)
=-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
(where o is dot product.)
=-h(cos(theta)<i:3>-<j:3>)
=h(<j:3>-cos(theta)<i:3>) m


The result is a rectangle, not the original parallelogram. We
can test the result.


h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3>


The magnitude of the area vector is conserved, but the direction
is opposite.


The mass of a round plate is M kg, and the area vector is
A m^2<i:3>; then the surface mass density is


M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3>


4. Mass vector in physics.


Mass vector has been found in two equations: 1) the velocity
equation of string. 2) Bernoulli's equation.


i) For waves on a string, we have the velocity equation:


v=sqrt(tau/mu). v is velocity of wave, tau is tension
applying to string, and mu is linear mass density of
string. We can rewrite the equation:


mu=tau/v^2.


In the above equation, the mu is parallel to tau, and both
of them are vector.


ii) Bernoulli's equation is:


P + k*v^2/2=C (P is pressure, k is volume density, and v is
velocity. Here we neglect the gravitational term.)


Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's
equation(where <i:3> is a unit vector),


P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3>
F<i:3> + L<i:3>*v^2/2=C*A<i:3>
(where F is the magnitude of force, and L is the magnitude
of linear mass density.)


These two equations are well used in the theory "Magnetic force:
Combining Drag force and Bernoulli force of ether dynamics."
For detail, please refer to my site:
http://www.geocities.com/redlorikee

From: Eric Gisse on

Danny Dot wrote:
> --
> Danny Dot
> Look at my site and see how NASA treats a creative mind!!!
> The summary is "Not Very Well" :-)
> www.mobbinggonemad.org

How nice of you to put a sig at the beginning and end of your post.
Just in case we can't figure out who is talking.

>
>
> "Ka-In Yen" <yenkain(a)yahoo.com.tw> wrote in message
> news:1156469606.545703.194940(a)i42g2000cwa.googlegroups.com...
> >
> > Home work for Eric Gisse:
> > A rectangle sits in 3D space. The area vector of the rectangle is A,
> > and the legth vector of one side of the rectangle is L. Please find
> > the length vector of the other side of the rectangle?
> >
>
> I have always thought of mass as a scalar, not a vector. Momentum is a
> vector, but not mass. Maybe I am wrong.

Mass is a scalar. Momentum is a vector. Length is a scalar.

Wasn't that easy?

>
> Danny Dot
> www.mobbinggonemad.org

From: Ka-In Yen on

Ka-In Yen wrote:
> Danny Dot wrote:
> > --
> > Danny Dot
> > Look at my site and see how NASA treats a creative mind!!!
> > The summary is "Not Very Well" :-)
> > www.mobbinggonemad.org
> >
> >
> > "Ka-In Yen" <yenkain(a)yahoo.com.tw> wrote in message
> > news:1156469606.545703.194940(a)i42g2000cwa.googlegroups.com...
> > >
> > > Home work for Eric Gisse:
> > > A rectangle sits in 3D space. The area vector of the rectangle is A,
> > > and the legth vector of one side of the rectangle is L. Please find
> > > the length vector of the other side of the rectangle?
> > >
> >
> > I have always thought of mass as a scalar, not a vector. Momentum is a
> > vector, but not mass. Maybe I am wrong.
> >
> Dear Danny Dot,
>
> Thank you for your comment. You are right; mass is scalar.
> In three dimensional vector algebra, linear mass density and
> surface mass density are vectors; shortly I call them mass
> vector.
>

Dear Danny Dot,

Do you have any comment on the paper "Magnetic force:
Combining Drag force and Bernoulli force of ether dynamics"?
http://www.geocities.com/redlorikee/mdb2.html

If you find any flaws of the theory, please kindly advise me.

From: Ka-In Yen on
Physicists recall. A fault is found in their logic circuit: they are
ill-trained in
3D vector algebra.


The proof of mass vector.

Ka-In Yen
http://www.geocities.com/redlorikee


Introduction:
In this paper, we will prove that linear mass density and
surface mass density are vector, and the application of mass
vector is presented.


1. The unit of vector.


In physics, The unit of three-dimensional cartesian coordinate
systems is meter. In this paper, a point of 3-D coordinate
system is written as


(p1,p2,p3) m, or (p:3) m


and a vector is written as


<a,b,c> m, or <a:3> m


or


l m<i,j,k> = <a,b,c> m


where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
and <i,j,k> is a unit vector which gives the direction of
the vector.


For three reasons, a magnitude of a vector can not add to a
scalar:
i) The magnitude belongs to the set of vector; it's a
portion of a vector. Scalar belongs to a field.
ii) The magnitude is real non-negative number, but scalar
is real number.
iii) The unit of magnitude is meter, but scalar has no unit.
This is a major difference between physics and mathematics.
5m+3 is meaningless.


2. Linear mass density is a vector.


The mass of a string is M kg, and the length of the string
is l m<i:3>. Where l m is the magnitude of the length, and
<i:3> is a 3-D unit vector which gives the direction of the
string. Then the linear mass density of the string is:


M/(l<i:3>)=(M/l) (kg/m)<i:3>


The direction, <i:3>, is not changed by "division", so we
can move <i:3> from denominator to numerator. A direction
is changed by -1 only. A proof is found in Clifford algebras:


[Proof]
k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
=(k/l) <i,j,k>
where l is the magnitude of <a,b,c>, and <i,j,k> is the
unit vector of <a,b,c>.
[Proof]


3. Surface mass density is a vector.


A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
and <j:3> are unit vectors. The area vector of the parallelogram
is the cross product of these two vectors.


l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
= lh abs(sin(theta)) (m^2)<k:3>


Where theta is the angle between <i:3> and <j:3>. <k:3> is
a unit vector which is perpendicular to <i:3> and <j:3>.
For AXB=-BXA, an area has two directions.


We can divide the area vector by the length vector.


lh*abs(sin(theta))<k:3>/[l<i:3>]
=h<i:3>X<j:3>/<i:3>
=h(<i:3>X<j:3>)X<i:3>
(The direction, <i:3>, is not changed by "division", and
the division is replaced by a cross product.)
=-h<i:3>X(<i:3>X<j:3>)
=-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
(where o is dot product.)
=-h(cos(theta)<i:3>-<j:3>)
=h(<j:3>-cos(theta)<i:3>) m


The result is a rectangle, not the original parallelogram. We
can test the result.


h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3>


The magnitude of the area vector is conserved, but the direction
is opposite.


The mass of a round plate is M kg, and the area vector is
A m^2<i:3>; then the surface mass density is


M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3>


4. Mass vector in physics.


Mass vector has been found in two equations: 1) the velocity
equation of string. 2) Bernoulli's equation.


i) For waves on a string, we have the velocity equation:


v=sqrt(tau/mu). v is velocity of wave, tau is tension
applying to string, and mu is linear mass density of
string. We can rewrite the equation:


mu=tau/v^2.


In the above equation, the mu is parallel to tau, and both
of them are vector.


ii) Bernoulli's equation is:


P + k*v^2/2=C (P is pressure, k is volume density, and v is
velocity. Here we neglect the gravitational term.)


Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's
equation(where <i:3> is a unit vector),


P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3>
F<i:3> + L<i:3>*v^2/2=C*A<i:3>
(where F is the magnitude of force, and L is the magnitude
of linear mass density.)


These two equations are well used in the theory "Magnetic force:
Combining Drag force and Bernoulli force of ether dynamics."
For detail, please refer to my site:
http://www.geocities.com/redlorikee

From: Eric Gisse on

Ka-In Yen wrote:
> Physicists recall. A fault is found in their logic circuit: they are
> ill-trained in
> 3D vector algebra.

Says the guy who can't use the standard notation to save his life.

[snip stupidity]

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