Phys211C1 p1 Physical Quantities and Measurement What is Physics? Natural Philosophy science of matter and energy fundamental principles of engineering and technology an experimental science: theory  experiment simplified models range of validity size speed Classical Mechanics Quantum Mechanics Relativistic Mechanics Quantum Field Theory

Phys211C1 p2 Quantifying predictions and observations physical quantities: numbers used to describe physical phenomena height, weight e.g. may be defined operationally standard units: International System (SI aka Metric) defined units established in terms of a physical quantity derived units established as algebraic combinations of other units

Phys211C1 p3 Scientific Notation: powers of 10 5,820 = 5.82x10 3 = 5.82E = 5.28x10 -4 = 5.28E-4 note: 10 3 = 1x10 3 =1E3 not 10E3! How big (in terms of everyday life/other things) is a meter nanometer gram centimeter kilometer kilogram Common prefixes

Phys211C1 p4 Dimensional Analysis: consistency of units Algebraic equations must always be dimensionally consistent. You can’t add apples and oranges! converting units treat units as algebraic quantities multiplying or dividing a quantity by 1 does not affect its value

Phys211C1 p5 Units Conversion Examples Example 1-1 The world speed record, set in 1983 is km/hr. Express this speed in m/s Example how man cubic inches are there in a 2 liter engine? Some Useful Conversion factors: 1 inch= 2.54 cm 1 m = 3.28 ft 1 mile= 5280 ft 1 mile = 1.61 km

Phys211C1 p6 Significant Figures and Uncertainty Every measurement of a physical quantity involves some error random error averages out small random error  accurate measurement systematic error does not average out small systematic error  precise measurement less precise less accurate

Phys211C1 p7 Indicating the accuracy of a number: x ±  x or x±  x nominal value: the indicated result of the measurement numerical uncertainty: how much the “actual value” might be expected to differ from the nominal value sometimes called the numerical error 1 standard deviation A measured length of 20.3 cm ±.5 cm means that the actual length is expected to lie between 19.8 cm and 20.8 cm. It has a nominal value of x = 20.3 cm with an uncertainty of  x.5 cm. fractional uncertainty: the fraction of the nominal value corresponding to the numerical uncertainty percentage uncertainty: the percentage of the nominal value corresponding to the numerical uncertainty

Phys211C1 p8 Uncertainties in calculations Adding and subtracting: add numerical uncertainty Multiplying or Dividing: add fractional/percentage uncertainty Powers are “multiple multiplications”

Phys211C1 p9 More complex algebraic expressions must be broken down operation by operation a = 3.13±.05 b = 7.14 ±.01 c = ±.2%

Phys211C1 p10 Significant Figures: common way of implicitly indicating uncertainty number is only expressed using meaningful digits (sig. figs.) last digit (the least significant digit = lsd) is uncertain 3one digit 3.0two digits (two significant figures = 2 sig. figs.) 3.00 three digits,etc.(300 how many digits?) Combining numbers with significant digits Addition and Subtraction: least significant digit determined by decimal places (result is rounded) =.87 = =  6.43 =  6.4 Multiplication and Division: number of significant figures is the number of sig. figs. of the factor with the fewest sig. figs. 1.3x7.24 = = /.3794 = = 46.1 Integer factors and geometric factors (such as  ) have infinite precision  x = = 44.4

Phys211C1 p11 Estimates and Order of magnitude calculations an order of magnitude is a (rounded) 1 sig fig calculation, whose answer is expressed as the nearest power of 10. Estimates should be done “in your head” check against calculator mistakes! Additional Homework: with a = 3.13±.05 b = 7.14 ±.01 c = ±.2% evaluate expressions (nominal value and uncertainty expressed as numerical uncertainty and percentage uncertainty)