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motion: TOC for Knowledge Concepts, Exercises, and Solutions

Recall that a circle has 2 pi radians (pi ~ 3.1416).  A circle also has 360 
degrees.  Both degrees and radians measure arc. This means that a radian is about 
57.3 degrees.

    ---------- = 57.3 degrees in a radian.
     2 * 3.14

So, we can convert back and forth easily between units of arc.
Recall also that one degree is 60 arcminutes, and that one arcminute is 60 
arcseconds.  So one degree is 3600 arcseconds, and one radian is about 206,000 

When looking up at the sky to measure things, it's useful to keep in mind that a 
fully open, outstretched hand spans about 20 degrees of arc from tip of thumb to 
tip of pinky.  A closed hand spans about 10 degrees and a finger width is about 2 

Here is one very useful thing about radians: an object that subtends one radian of 
arc is as wide as it is far away.  For example, if you're 15 feet away from a car, 
and the car is 15 feet long, then the car subtends one radian of arc.

Here is another very useful thing about angles and arcs: ratios are preserved when 
it comes to angles.  So if you double your distance from an object, the projected 
size is cut in half. If you triple your distance, the projected angle is cut to a 
third.  If the car above is 30 feet away, then it subtends half a radian of arc; 
if it's 45 feet away, it subtends a third a radian; etc.  This also works for 
degrees of arc, arcminutes, and arcseconds.