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hl physics 2nd edition.pdf


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01

Measurements and uncertainties
Making observations
Before we can try to understand the Universe we have to observe it. Imagine you are a
cave man/woman looking up into the sky at night. You would see lots of bright points
scattered about (assuming it is not cloudy). The points are not the same but how can
you describe the differences between them? One of the main differences is that you
have to move your head to see different examples. This might lead you to define their
position. Occasionally you might notice a star flashing so would realize that there are
also differences not associated with position, leading to the concept of time. If you
shift your attention to the world around you you’ll be able to make further close-range
observations. Picking up rocks you notice some are easy to pick up while others are
more difficult; some are hot, some are cold, and different rocks are different colours.
These observations are just the start: to be able to understand how these quantities are
related you need to measure them but before you do that you need to be able to count.

Figure 1.1 Making
observations came
before science.

If the system of numbers
had been totally different,
would our models of the
Universe be the same?

Numbers
Numbers weren’t originally designed for use by physics students: they were for
counting objects.
2 apples + 3 apples = 5 apples
2 + 3 = 5
2 × 3 apples = 6 apples
6 apples
2  = 3 apples
So the numbers mirror what is happening to the apples. However, you have to be
careful: you can do some operations with numbers that are not possible with apples.
For example:
(2 apples)2 = 4 square apples?

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