What is the meaning of change of angular momentum of a ballistic object during its flight?

Question

In a 2D world, three stones, whose magnitude of initial velocities are 5000m/s, are thrown from the North pole towards the Equator with horizontal initial angles of 15^o, 30^o, 45^o and 60^o angles. Their trajectories are as below:

Their respective angular momentums untill they fall to the ground are as below:

I'm not a physicist, I'm a grad student in Electronics Engineer and I'm very unfamiliar to the term "momentum". This homework is about controlling flight of aerial objects. I only know angular momentum as a quantity that is product of mass and speed. I did my assignment up to this point. And now, I have to make some comments on it. But those curves of angular momentum doesn't mean anything to me.

What should I write in my report? Why is angular starting from a different positive value for each stone, and then decreasing in time, finally rising up to its initial value when the stone falls on the ground? What is the meaning of this physical phenomenon?

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EDIT:

I iterated these two differential equations:

$ \ddot{r} - r\dot{\theta}^2 + \frac{GM}{r^2} = 0 \\ \frac{d}{dt}(r^2\dot{\theta}) = 2r\dot{r}\dot{\theta} + r^2\ddot{\theta} = 0 $

With initial conditions:

$ r = R_0 \\ \theta = \frac{\pi}{2} \\ \dot{r} = 5000 sin(\gamma) \\ \dot{\theta} = -\frac{5000 cos(\gamma)}{R_0} \\ $

Where;
$ R_0 = 6378000 m $ (radius of the Earth)
$ G = 6.6742 \times 10^{-11} N (\frac{m}{kg})^2 $ (the gravitation constant)
$ M = 5.9722 \times 10^{24} kg $ (mass of the Earth)
$ \lambda = 15^o, 30^o, 45^o, 60^o $ (launch angles for each stone)

At each iteration step, I calculated the angular momentum per unit mass by the following formula:

$ \mbox{Angular Momentum per Unit Mass} = r \dot{\theta}^2 $

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EDIT 2:

I realized that I was wrong with the formula of angular momentum per unit mass. I must have been:

$ \mbox{Angular Momentum per Unit Mass} = r^2 \dot{\theta} $

When I modified the formula, I obtained these curves below in which angular momentum stays constant:

Answer 1

Momentum, being it angular or not, is as you mentioned a product of mass and velocity. Intuitively it is a measurement of how much force it takes to change the way that object is moving (and the time you must apply that force for). For linear momentum, a flying cannonball is harder to stop than a ping pong ball, even if they're moving at the same speed. This is intuitive indeed, since you realize that the ping pong ball will be stopped quickly just by air resistance, whereas the cannonball will travel much further.

Angular momentum is the same concept but for rotation - how much Torque (angular force) does it take to change the spin on an object. I'm not totally clear from your post in which direction the object is rotating, but I hope the intuition helps. If the angular momenta remain constant throughout the flight of the object, that means that they are spinning constantly as they move through the air. Imagine throwing a ball and putting "backspin" on it.