‫However, what if I sex now equals two kilograms times meter squared, then I y y equals.
‫Three kg tanks, meter squared.
‫And ices equals five kilograms times meter squared and 5.8 feet on that and side that are still equal.
‫And there are one radians per second, then h x, h y and z equal the mass moment of inertia matrix
‫times.
‫The angular velocity vector and you're left with two, three and five kg meter squared per second.
‫Now you can clearly see that the angular momentum vector and the angular velocity vector.
‫They have different directions, and that's because you can't extract that constant anymore.
‫You can see that the vector one one one clearly has a different direction compared to a vector that
‫has elements two, three and five.
‫And you can imagine that things can be even worse if you're products of inertia are not zeros.
‫In general, if you have an object and your angular momentum, vector has a different direction compared
‫to your angular velocity vector, then that's not good.
‫Because that will make the rotation of the object not stable.
‫The rotation will not be about any consistent direction, it will tumble.
‫Meaning that at some point your angular velocity will be in this direction.
‫Then at another point, it will be in this direction.
‫And then maybe in this direction.
‫So when you're dealing with rotations in 3-D, then it is recommended that you design your things in
‫such a way that your angular momentum vector would be as closely as possible to your angular velocity
‫vector so that you wouldn't have big differences there and you could achieve that by, for example,
‫only rotating about one axis.
‫Let's say that you only rotate about x axis and you make the y axis and z axis rotations zero gradients
‫per second.
‫In that case, you will have two here.
‫But here you will have zero.
‫And here you will have zero as well.
‫And then your angular velocity vector is one zero zero and then your angular momentum vector is two
‫zero zero, and then they are in the same direction in the X direction.
‫And that makes the rotation much more stable.
‫So now that you know what angular momentum is, we can look at the law that allows us to derive equations
‫of motion for the rotational motion.