Question

How do I compute the change in angular momentum of a system of random rigid bodies?

Answer 1

For clearity: the bodies are not point masses. Each has it's own moment of inertia.

Answer 2

Work out each angular momentum using the easiest formula at hand, then add them all up (as vectors).

Answer 3

But that depends on if the bodies are just rotating or they are translating as well..

if they are just rotating about their CM then.. what Vincent said would hold.

else wouldn't it be enormosuly complicated? :P.. cause it ll vary with the point of reference?

Answer 4

Well, each problem has an optimal way of computing such a quantity.
If some parts have translation, then add up their translational angular momentum.

Answer 5

In my dynamics notes I have written the following:
$$\frac{d\vec{p}_A}{dt}= \sum\vec{AC_i}\times m\vec{a_{ci}} + \sum \frac{dR_i}{dt}\left\{{I^{(i)}_{ci}}{\omega}^{(i)}_{ci}\right\}+\sum R\left\{{I^{(i)}_{ci}}\frac{d{\omega}^{(i)}_{ci}}{dt}\right\}$$
where $A$ is a random point, $C_i$ the center of mass of object $i$, $\left\{{I^{(i)}_{ci}}{\omega}^{(i)}_{ci}\right\}$ (an admittedly strange notation for) the resulting vector from $I_{i}\vec{\omega_{ci}}$ if $I_{i}$ is a diagonal matrix and $R_i$ a matrix that projects object $i$ to its principal axes of inertia. I am, however, incapable of finding my derivation of this formula.

Answer 6

just take out the moment of inertia of the body and u r done\[L=I\] and u know the angular velocity of the body

Answer 7

\[L=I\]

Answer 8

L=(moment of inertia )(angular velocity)

Answer 9

I take it that by "moment of inertia" you mean "the moment of inertia around the point that is asked (point A)", but this moment of inertia is never known. In reality you only know the moment of inertia around it's principle axes..

Answer 10

you can find moment of inertia about any point if u use parallel axis theorem and perpendicular axis theorem.

Answer 11

Ok, I realize this is very dumb and probably annoying, but I actually forgot to write "change of" in the title question. I am looking for the CHANGE of angular momentum. My apologies for that.

Answer 12

hmmm.....which one is varying....angular velocity or moment of inertia?

Answer 13

both: I would think that the angular velocity changes by angular acceleration and that the moment of inertia changes due to instantaneous displacement and rotation of the object (the rotation also makes that dR/dt is non-zero)

Answer 14

then u have to find initial and final M.I. and angular velocity. and then u know.If u take vectors then u'll get also directions

Answer 15

Presumably, you are applying a torque somehow to cause a change in angular momentum; else, it would be constant.