is it time to mention tonearm's length again?

Hi folks,
I looked over quite a few posts related to the subject, tons of intricacies again which is great!
But one thing slipped my understanding, sorry, I am a little slow last ten years.
What I can not figure is - why longer arm helps traction (between the tip and the record). Or more to the point - I would think that the traction will be minimal when the tip's axis (provided such exists) is perpendicular to the line going from the tip to the spindle. I probably should know more about how the tip is built - in other words whether it does matter or not how the cartridge (and the tip) is positioned. But I thought the groove should go "along the cartridge". Now if as in my case the distance between the center of the arm base and the center of the disk is 9 inch and the tonearm is 12 inch long then the angle between the tonearm line and the line going to the center of the record becomes less then 90 degrees.
In the above example then with 12 inch arm - does it make sense to rotate the cartridge clockwise a little on the tonearm to get that angle back to 90 degrees? If above makes sense at all.
Sorry for the lengthy email. And thanks for your time.

Anatoliy