So far so good but what happens if we change the rotation axis? That is, let’s untape the pencil and tape it back in a different position. The extreme change will be to rotate the pencil through an angle of 90 degrees while keeping the rectangle fixed. Angles are commonly measured in units of degrees or radians. By definition, there are 360 degrees in a circle. What this means is that if we draw a circle and slice it into 360 equal “pie” slices then each slice is one degree wide. 90 slices all pushed together to form one big slice, would form a 90 degree angle. If we had two pencils and rotated one by 90 degrees while keeping the other fixed we would get something like this

A 90 degree angle is called a “right angle” and when two lines or axis are rotated 90 degrees with respect to each other they are said to be perpendicular (or more abstractly, in math, they are said to be orthogonal).

[A brief aside, you can skip this and read it later: Learning about angles will be very useful to you when you use your telescope. Astronomers use angle measurements to specify where to find things in the sky. A few examples may help. An imaginary slice of sky with your eye at one end and the sides of the moon at the other end is about one half degree wide. If you hold your fist out at arm's length the slice formed by your eye and the sides of your fist is approximately 10 degrees. For many purposes, like astronomy, degrees are just too coarse a measurement so each degree is further sliced into smaller pie shapes called arc minutes and each arc minute is sliced into even smaller segments called arc seconds. Go to the "Angles in the Sky" website to learn more about this.

The use of the words minutes and seconds is not accidental. It is related to the rotation of the Earth about its' polar axis which for all practical purposes is a constant which is why a day is 24 hours long. This illustrates an important point which we will encounter again and again. In math and science often we will use ordinary words to describe something but the meaning of those words in science will be completely different from ordinary, every day usage!]

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Tags: Physics, Science

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