# 1: Units, Dimensions, and Scaling Arguments

{'English - US': '/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-1/lec1-edit.srt'}

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Topics covered: This lecture is about units, dimensions, measurements and associated uncertainties, dimensional analysis, and scaling arguments.

Instructor/speaker: Prof. Walter Lewin

Date recorded: September 8, 1999

## Video Index

Please make sure you play the Video before clicking the links below.

• Fundamental Units
The fundamental units are length, time and mass.

• Discussion of 'Powers of Ten'
'The Powers of Ten' (© Charles & Ray Eames and Pyramid Media) movie, covering 40 orders of magnitude, has been removed from the video for reasons of copyright.

• Dimensions
Dimensions are denoted with brackets; some examples are given.

• The Art of Making Measurements
A measurement is meaningless without knowledge of its uncertainty. The lengths of an aluminum rod and the length of a student are both measured standing straight up and lying down horizontally to test whether the student's length is larger when he is lying down than when he is standing straight up. Within the uncertainty of the measurements, the difference between standing and lying is substantial for the student (NOT for the aluminum rod).

• Was Galileo Galilei's Reasoning Correct?
Why are mammals as large as they are, and not much larger? The argument suggests that if they become too heavy, the bones will shatter. Galileo Galilei suggested that material properties of our bones impose a natural limit on the size of things. Professor Lewin brings this to a test by presenting Galilei's scaling arguments, and he compares them with actual measurements.

• Dimensional Analysis
The dimensions of both sides of the equation must be the same; this is non-negotiable in physics. Using this idea, Professor Lewin reasons that the time for an object to fall from a certain height is independent of its mass and proportional to the square root of the height from which it is dropped. He confirms this conclusion by dropping an apple from 3.000 m and 1.500 m with an uncertainty in each of 3 mm. He then shows why his "prediction" was a cheat.