Away From the Pole, Not Up the Page

You'll learnto separate a polar point's radial motion from its angular motion.

A point on a polar curve does two things at once: the angle carries it counterclockwise, and r decides whether it is drifting toward the pole or away from it. While r is positive, rising r means away. It does not mean up, it does not mean faster, and it says nothing about which way the sweep turns. Distance from the pole is |r|, so once r goes negative a falling r and a growing distance happen together.

8 STEPS · 6 QUICK CHECKS · TOWARD · AWAY · RATE PER RADIAN · NEGATIVE r · v3

|r| is a distance, not an altitude

Before you start

What you're looking at

A point on one fixed ray whose radius simply increases — moving away from the pole.

The question

Is the point drifting toward the pole or away from it?

Watch for

Radius growing (away) and shrinking (toward) on a fixed ray before any angle motion is added — while r is positive, rising r means away, not up. Step 5 takes r past zero, where that shortcut stops working.

Step 1 / 8