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# Inertia & mass

Throw around with stuff and you quickly realize that some stuff is “tougher” than other. Not just from being bigger but really from being “tougher” to tumble and throw about.

• Throw a bowling ball and a basketball. Same size. But the bowling ball is undoubtedly much “tougher” to speed up. Much “tougher” to accelerate.
• Spin a bike wheel and an iron flywheel. Same size. But the flywheel is much “tougher” to start spinning.

Why don’t we call such “toughness” inertia.1

We have two types of inertia here: inertia when throwing and inertia when spinning. ‘Spinning’ belongs to the Rotation discipline later; let’s here first look at ‘throwing’. Let’s call such “throwing toughness” mass with the symbol $m$.

Mass clearly counteracts a throw, meaning it counteracts a force. Mass basically seems to be a force “dampener”: When a force pushes or pulls, the mass “dampens” its effect. Mass seems to be a new fundamental property. So, to talk about ‘how much mass’ we have, let’s invent a new fundamental unit for it: why not gram with the symbol $\mathrm g$.2 3

As with the metre and the second, we now must decide what ‘one gram’ should be.

• 1 metre’ was chosen as some arbitrary length,
• 1 second’ as some arbitrary duration, and similarly
• 1 gram’ is just some small amount of mass, which someone back in time chose for some reason.4

Note: For some odd reason it was previously officially decided that the SI base unit for mass should not be just the gram $\mathrm g$ but rather the kilogram $\mathrm{kg}$.[4] 1 kilogram is 1000 grams; not a new symbol, just the gram added a ‘kilo-’ prefix. Maybe ‘kilograms’ (‘kilos’ as we say in everyday life) felt more useful at the time.5 We’ll keep this fact in mind for the future.

To get a feeling of the gram, here is a short overview of the scale:

Mass scale
$\vdots$
GigagramsSpace crafts8
MegagramsA bull[11]
KilogramsGroceries
GramsA Dollar bill
MilligramsInsects7
MicrogramsAn eyelash6
NanogramsHuman cells[6,7]
$\vdots$

References:

1. Online Etymology Dictionary’ (dictionary), Douglas Harper, www.etymonline.com
2. Water - Density, Specific Weight and Thermal Expansion Coefficient’ (web page), The Engineering Toolbox, 2003, www.engineeringtoolbox.com/water-density-specific-weight-d_595.html (accessed Sep. 27th, 2019)
3. Collection complète des lois, décrets, ordonnances, règlemens avis du Conseil d’état’ (book), Library of Princeton University, 37th ed., vol. 6, 1834, books.google.ch/books?id=0mYZAAAAYAAJ&pg=PA70 (accessed Sep. 27th, 2019)
4. The International System of Units (SI)’ (book), B. Inglis, J. Ullrich and others, Bureau International des Poids et Mesures (BIPM), 9th ed., 2019, www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf, chapter 3
5. The name “kilogram”: a historical quirk’ (web page), Bureau International des Poids et Mesures (BIPM), www.bipm.org/en/measurement-units/history-si/name-kg.html (accessed Sep. 11th, 2019)
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