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Skill 7 of 9
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# Momentum

• Carrying a tomato takes effort due to its weight.
• Catching a tomato takes more effort due to not only its weight but also the impact between tomato and hand.

How can we understand that impact? What makes the impact tougher and requiring extra effort?

It seems that the, shall we say, “amount of motion” that the falling apple “has” or “carries” causes extra toughness. And this “amount of motion” is clearly not just velocity $\vec v$: a heavier apple is even tougher to catch, so mass $m$ seems to be involved as well. Both the ‘how fast’ and the ‘how tough to stop’ seem to be a part of an object’s “amount of motion”.1

Instead of “amount of motion”, let’s invent a proper property name for it, such as momentum.2 And let’s give it the symbol $\vec p$:[4] 3 4

$$\vec p=m\vec v$$

With this formula, the unit of momentum $\vec p$ is of course that of ‘mass units times velocity units’: $\mathrm{[kg\cdot m/s]}$.

References:

1. bevægelsesmængde’ (dictionary, in Danish), Henrik Smith, Den Store Danske, Gyldendal, denstoredanske.dk/index.php?sideId=46610 (accessed Apr. 10th, 2020)
2. Impuls (bevægelsesmængde)’ (web page, in Danish), Cecilia Mortensen Kobæk, Fysikleksikon, Niels Bohr Institute, Copenhagen University, 2009, fysikleksikon.nbi.ku.dk/i/impuls (accessed Apr. 10th, 2020)
3. momentum’ (dictionary), Collins Dictionary, HarperCollins Publishers, www.collinsdictionary.com/dictionary/english-french/momentum (accessed Apr. 10th, 2020)
4. Sears and Zemansky’s Univesity Physics with Modern Physics’ (book), Hugh D. Young & Roger A. Freedman, Pearson Education, 13th ed., 2012
5. Philosophiæ Naturalis Principia Mathematica’ (book, English translation published 1728), Isaac Newton, 1st ed., vol. 1, 1687, en.wikisource.org/wiki/Page:Newton%27s_Principia_(1846).djvu/89 (accessed Sep. 27th, 2019)
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