System of two bodies simple dynamics calculaton

[twowheelsbg]

Homework Statement

In a two-dimensional space there is a system of two bodies,
masses M1, M2, and coordinates (X1,Z1) and (X2,Z2)

I have to find total mass, its coordinates, inertia momentum, and angular momentum

Homework Equations

... my memories help here, obviously not so good ...

The Attempt at a Solution

total mass M=M1+M2

coordinates X=(X1*M1+X2*M2)/(M1+M2)
Z=(Z1*M1+Z2*M2)/(M1+M2)

Inertia momentum
first i calculate radius vectors R1=sqrt(X1*X1+Z1*Z1)
R2=sqrt(X2*X2+Z2*Z2)
then inertia momentums I1=M1*R1*R1
I2=M2*R2*R2,

and total inertia momentum I=I1+I2,
and here I tried to recheck my result other way:
common radius as R=sqrt(X*X+Z*Z), and inertia as I=(M1+M2)*R*R,
but the result was different which puzzled me ...
I am more close to first approach, but why second is not correct ?

 

[twowheelsbg]

Actually I made a step forward,
explaining my mess some questions dropped

Sorry first for the incomplete thesis, I just tried to keep it simple.
There is a third axle 'Y' of course, which absence makes questions of momentums irrelevant.

I also comprehended why second approach is not so good, as the system inertia moment
strongly depends of masses positioning ...

So currently I am wondering how to calculate system's angular momentum ( via Y axis ) ...

 

[uriwolln]

I was wondering, how can you have momentum if nothing is moving?

 

[twowheelsbg]

Actually you are right Uriwolln, it it more complicated.
Both masses have particular equations and their coordinates (X,Z) vary with time.
My final goal is to calculate their angular momentum via Y axis,
and after it's derivative, which is to be used as equal to external moments
applied to the system via Y axis.

That's why I ask in general how to find angular momentum via Y axis,
hope to complete math myself and not to bother people trying to help me here.

 

[uriwolln]

In general angular momentum defined as:
L=R x P
Where P is the momentum, thus P=mv.
Bare in mind that 'x' means cross, so make sure R and P that you will use are perpendicular to one another.

 

[gneill]

In general angular momentum defined as:
L=R x P
Where P is the momentum, thus P=mv.
Bare in mind that 'x' means cross, so make sure R and P that you will use are perpendicular to one another.

Or, if at some particular instant you have a position vector R and a velocity vector V, then L = m(R x V), which can be done in component form easily enough. No need to worry about them being perpendicular if you do the full cross product.

 

[twowheelsbg]

Thank you guys, for the directions, I solved the problem exactly this way -
I saw that words for the physical terms into my writing became links,
and followed them to library, where it was explained more in details how to solve for
angular momentum - special thanks to forum architects and contributors