1
$\begingroup$

I'm having a bit of confusion about why I can use the average force to compute the angular frequency in the given example:

We have a billiard ball, and hit it with a cue 2/3 under the middle of the ball. Given are the moment of inertia, the radius and the velocity right after the hit.

The hint suggests that I use the average force to calculate the angular frequency at the beginning.

So my question would be: Why am I allowed to do that? Does the force applied at the beginning to the ball equal a situation where I`m applying the average force constantly to the ball? If yes, how can I prove that mathematically?

Thank you in advance!

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

It's a necessary simplification, since you do not have information that would allow you to determine exactly how the force varies over time. This would require consideration of elastic deformation, via some highly non-trivial analysis, eventually using a finite-element approach, most probably.

Improve this answer
$\endgroup$
2
  • $\begingroup$ I understand that much as well. But I want to know why it works and why I`m allowed to use that :D Do you have an answer for that as well? :) $\endgroup$
    – Yalom
    Commented Jan 19, 2017 at 9:00
  • $\begingroup$ Whats up in general with these averages? Cause e.g. While calculating the equastion of motion of a damped oscillator whe use the averag forces as well: We say that the position of the mass depends only on the average spring force devided with the average friction force. WHY can we do that HERE as well? $\endgroup$
    – Yalom
    Commented Jan 19, 2017 at 9:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.