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Physical Measurements

Prof. Yury Kolomensky01/19/2007

-Physical measurements-Units-Precision of measurements, significant digits-Estimation, order of magnitude

01/17/2007 YGK, Physics 8A

Physics is Experimental Science• Driven by observations (phenomena) and

measurements (quantities) Relate quantities to each other thru a (finite) set of relations

(formulae) (Most) physics laws are expressed mathematically

Make quantitative predictions• Quantities that are not observable are not relevant• Laws (theories) that are not verifiable experimentally

or by observation are not relevant


Example: Position vs Time


Units• Express each quantity in terms of a well-

defined (and agreed-upon) standard Apples with apples, Becquerels with Becquerels

• Base units: Distance [L], Mass [M], Time [T] In mechanics, everything else can be expressed in

terms of these


SI (Metric) System• International System of Units

[L] = 1 meter (metre, m) [M] = 1 kilogram (kg) [T] = 1 second (sec, s) MKS

• Compound (derived) units [F] = 1 Newton (N) = 1 kg*m/s2

• Metric system (derived units in decimalpowers)


Full Set of SI Units


Some Derived Units


SI Prefixes


A

C

B

earth

equator

In 1792 the meter was defined to be 10-7 of the distancefrom the north pole to the equator along the Paris meridian(the Rose Line, for you “The Da Vinci Code” fans)

For practical reasons the meter was later defined as thedistance between two fine lines on a standard meter barmade of platinum-iridium (and kept in Paris).

Since 1983 the meter is defined as the length traveled bylight in vacuum during the time interval of1/299792458 of a second.

71 m

10

AB!

The Meter


Initial (astronomical) definition:

Since 1967: 1 s = the time taken by9192631770 light oscillations of a particularwavelength emitted by a 133Cs atom. Goodto 5*10-12 (1 sec in 6000 years). Even betterprecision is now possible.

11 second

24 60 60

of the time it takes the earth

to complete a full rotation

about its axis

!" "

The Second


The SI standard of mass is a platinum-iridium cylinder. The cylinder is kept atthe International Bureau of Weights and Measures (near Paris) and assigned amass of 1 kilogram. Accurate copies have been sent to other countries.

The Kilogram

More practical: 1 kg ≈ mass of 1 liter of waterMore precise: 1 kg = 6.0221415(10)*1026 a.u.


The English System• Arcane and non-intuitive, but familiar :)

[L] = 1 ft (1’) = 12 in (12”) 1 yard = 3 ft, 1 mile = 5280 ft Conversion to metric: 1 in = 2.54 cm = 0.0254 m 1 mi = 1609 m, 1 yard = 0.91 m, 1 ft = 0.31 cm

[M] = 1 slug 1 slug = 1 lb/(1 ft/s2) = 14.6 kg

[T] = 1 s [F] = 1 lb 1 lb = 4.448 N = 0.454 kg * g


Unit Conversion

• Use relations between units and “rule of 1” 1 mi = 1609 m 1 = (1 mi)/(1609 m) = (1609 m)/(1 mi)

1 hr = 3600 s 1 = (1 hr)/(3600 s) = (3600 s)/(1 hr)

• Chain conversion65 mph = 29 m/s


Importance of Unit Conversion

• Gimli Glider (1983) kg vs lb in fuel density

• Mars Climate Orbiter (1999) Even rocket scientists make mistakes British vs Metric in navigation commands


Significant Figures and Precision

• Precision of measured quantities is important Instrumentation precision Approximations

Values assumed random within uncertainties

• Meaningless to quote numbers to more significantdigits than measured precision For compound quantities, error propagation rules apply

Relative precision for products, absolute precision for sums Keep appropriate number of significant digits (examples)


Some Well-Measured Quantities


Approximation and Estimation• Order of magnitude

Useful for computing things quickly π = 31 year = 3*107 sEquator circumference = 40,000 km c=1 (ft/nsec)

• Estimates(example)

physical measurements - university of california,...

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