IB Physics - Measurement and Uncertainty

SI Units System International 

• There are many types of units which are used to measure all types of quantities. Perhaps you know your weight in pounds, but would you know it in stone? A stone is one of a plethora of units used historically. (and still currently in some countries) Find out how much the unit "stone" is using this link http://www.unc.edu/~rowlett/units/index.html
• To standardize the units used to measure things an international agreement was made to use SI or System International. This system is accepted as standard in physics (and science) and will be the fundamental system of measurement for this course.
  • base units / derived units - http://physics.nist.gov/Document/SIDiagramBW.pdf or http://physics.nist.gov/Document/SIDiagramColor.pdf (in colour)
    • identify which base and derived units we will use in this course
  • defining base units; meter, second, kilogram - http://www.unc.edu/~rowlett/units/index.html
  • SI prefixes - http://www.unc.edu/~rowlett/units/prefixes.html

Exponential Notation (Scientific Notation)

• See appendix A-3 in text
• http://www.nyu.edu/pages/mathmol/textbook/scinot.html

Unit Conversion

• McCulloch method of converting any units (relates to dimensional analysis p1048 in text)
  • creating 1 from any equality
  • you can multiply anything by 1 without changing it
  • treat units as algebraic variables
• check your conversions using the web
  • http://www.onlineconversion.com/

Significant Digits

• rules
  • see text p7
  • see the rules in this link (better than text to describe issue of zero's)- http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm
• simple arithmetic - see link above
  • multiplication / division
  • addition / subtraction

Measuring Using a Vernier Scale

• http://www.physics.smu.edu/~scalise/apparatus/caliper/tutorial/
• http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html
• vernier.mcd

Dealing with Uncertainty

• Determination of Uncertainty
  • presumed from significant digits
  • from a measurment scale w.o. indicated uncertainty
  • from an instrument with a given uncertainty
• Types of Uncertainty
  • Indeterminate Errors - random errors
  • Determinate Errors - systematic errors
• Expression of Uncertainty
  • absolute
  • relative
    • fractional
    • %
• Propegation of Error - for details see link
  • When we use values which have uncertainties in calculations, the results of the calculation has an uncertainty value which is determined byt the uncertainty values in the calculations. The determination of the uncertainty of the results of a calculation from the uncertianties of values in a calculation is called Propagation of Errors. Actual propegation of error estimates are best done with advanced statistics and calculus. For IB we deal with a simplified form of propegation of errors. In general when dealing with uncertainty in calculations follow these rules;
    • Addition and Subtraction Rule - then add absolute uncertainty
    • Product and Quotient Rule - add relative uncertainty
    • Power Rule - for Q**P, (relative error in Q) * P (works for fractional or negative powers (eg. square root) as well)
  • This is not entirely correct, is inconsistent, and will result in gross over exagerations of error (where division occurs) in certain cases. Therefore when errors are determinate, the quotient rule should be modified. Modified Quotient Rule - the relative determinate error of the quotient is the relative determinate error of the numerator minus the relative determinate error of the denominator.This still presents problems when some errors are determinate and some are indeterminate in the same calculation. My understanding is that this modified rule is generally not taught in IB classes and it is unlikely to For this course use the basic rules above in exams and tests. There may be some labs however where you should consider using the modified rule above.