How Does Angular Momentum Conservation Affect Asteroid Collision Dynamics?

[Hak]

Continuing this discussion is pointless.

If a question says that radius is negligible then it means precisely this and nothing more: you do not need to include the radius anywhere in your calculations.

What it does NOT mean is that you can bring in a load of other information from outside the problem statement to decide whether you can omit any other variables from your calculations and make assumptions about what numerical range of error is permissible in an analytic solution (hint: none). If you do this then you will get the wrong answer.

Of course in this question it is nonsense to assume that the mass of the smaller asteroid is negligible: if it were then its angular momentum would also be negligible and the collision would have no effect on the rotation of the larger asteroid.

You got it wrong because you omitted a term you shouldn't have omitted. Don't waste your and everybody else's time trying to invent a justification for this, learn from your mistake and don't do it next time.

I am sorry to contradict you, but I guess you have not followed the whole discussion. I did not omit any terms that should not have been omitted, so I do not see where the error lies. I did not assume mass $m$ to be negligible in an absolute sense, but negligible with respect to mass $M$, which is a very different thing. The result itself is different, since it implies no zero angular momentum. If you follow the discussion from the beginning, you will see that far more authoritative people than myself, such as @haruspex, @Chestermiller, @PeroK and others have, before and better than me, advanced reasoning on the condition $m \ll M$. Only today I was made aware that this condition was not binding, because it was not part of the problem, but nevertheless it is in some respects reasonable, and not meaningless as you say. I do not understand why you made this criticism. I advise you to re-read all the previous posts, in no post is a result of a physical quantity of 0 implied.

 

[Frabjous]

I am sorry to contradict you, but I guess you have not followed the whole discussion. I did not omit any terms that should not have been omitted, so I do not see where the error lies. I did not assume mass $m$ to be negligible in an absolute sense, but negligible with respect to mass $M$, which is a very different thing. The result itself is different, since it implies no zero angular momentum. If you follow the discussion from the beginning, you will see that far more authoritative people than myself, such as @haruspex, @Chestermiller, @PeroK and others have, before and better than me, advanced reasoning on the condition $m \ll M$. Only today I was made aware that this condition was not binding, because it was not part of the problem, but nevertheless it is in some respects reasonable, and not meaningless as you say. I do not understand why you made this criticism.

@Hak Don’t argue with mentors or science advisors. They tend to stick together, and even when you win, you lose. Just move on to new physics questions.

 

[Hak]

@Hak Don’t argue with mentors or science advisors. They tend to stick together, and even when you win, you lose. Just move on to new physics questions.

All right, I apologise for any misbehaviour. It was not my intention to offend anyone, nor to create discord. Sorry again.

 

[erobz]

I wanted to clarify, though, that this is not homework or test preparation, it is just a problem that I am trying to dissect in every way possible and imaginable.

It's just unnecessary. You are going to have plenty of practice and chances to evolve your skillset in the peripheral physics surrounding the problem. It's not like educators give you a single problem each term...you get hundreds! If you are only 99% sure on some part you will get a hundred other chances to dive into it as you progress.

 

[Hak]

It's just unnecessary. You are going to have plenty of practice and chances to evolve your skillset in the peripheral physics surrounding the problem. It's not like educators give you a single problem each term...you get hundreds! If you are only 99% sure on some part you will get a hundred other chances to dive into it as you progress.

Thanks for your advice.

 

[haruspex]

You got it wrong

Why do you say that? In post #206, @Hak found $\omega$ correctly without making any approximation, beyond the given one that the size of the smaller object can be ignored.
The remaining question was how to find the subsequent centripetal force. For that, it is just a matter of finding the common mass centre. Because it had originally been stated that m<<M, it sufficed to take this as the centre of the larger body. It turned out that it had not been given that m<<M, yet the original author had made precisely that assumption.
So, in what sense has @Hak got it wrong?

Don't waste your and everybody else's time trying to invent a justification for this

I see no evidence of @Hak trying to justify any approximations or other doubtful steps. Quite the contrary; he has been trying to understand approximations that have been suggested.