College Physics Introductionand Chapter 1

Measurements Basis of testing theories in science Basis of testing theories in science Need to have consistent systems of units for the measurements Need to have consistent systems of units for the measurements Uncertainties are inherent Uncertainties are inherent Need rules for dealing with the uncertainties Need rules for dealing with the uncertainties

Systems of Measurement Standardized systems Standardized systems agreed upon by some authority, usually a governmental body agreed upon by some authority, usually a governmental body SI -- Systéme International SI -- Systéme International agreed to in 1960 by an international committee agreed to in 1960 by an international committee main system used in this text main system used in this text also called mks for the first letters in the units of the fundamental quantities also called mks for the first letters in the units of the fundamental quantities

Basic Quantities and Their Dimension Length [L] Length [L] Mass [M] Mass [M] Time [T] Time [T]

Standard Kilogram

Dimensional Analysis Technique to check the correctness of an equation Technique to check the correctness of an equation Dimensions (length, mass, time, combinations) can be treated as algebraic quantities Dimensions (length, mass, time, combinations) can be treated as algebraic quantities add, subtract, multiply, divide add, subtract, multiply, divide Both sides of equation must have the same dimensions Both sides of equation must have the same dimensions

Operations with Significant Figures Accuracy -- number of significant figures Accuracy -- number of significant figures When multiplying or dividing, round the result to the same accuracy as the least accurate measurement When multiplying or dividing, round the result to the same accuracy as the least accurate measurement When adding or subtracting, round the result to the smallest number of decimal places of any term in the sum When adding or subtracting, round the result to the smallest number of decimal places of any term in the sum

Conversions When units are not consistent, you may need to convert to appropriate ones When units are not consistent, you may need to convert to appropriate ones Units can be treated like algebraic quantities that can divide out Units can be treated like algebraic quantities that can divide out See the inside of the front cover for an extensive list of conversion factors See the inside of the front cover for an extensive list of conversion factors How Fast is 1 m/s?

Examples of various units measuring a quantity

Order of Magnitude Approximation based on a number of assumptions Approximation based on a number of assumptions may need to modify assumptions if more precise results are needed may need to modify assumptions if more precise results are needed Order of magnitude is the power of 10 that applies Order of magnitude is the power of 10 that applies

Cartesian coordinate system also called rectangular coordinate system also called rectangular coordinate system x- and y- axes x- and y- axes points are labeled (x,y) points are labeled (x,y)

Plane polar coordinate system origin and reference line are noted origin and reference line are noted point is distance r from the origin in the direction of angle , ccw from reference line point is distance r from the origin in the direction of angle , ccw from reference line points are labeled (r,  ) points are labeled (r,  )

Trigonometry Review

More Trigonometry Pythagorean Theorem Pythagorean Theorem To find an angle, you need the inverse trig function To find an angle, you need the inverse trig function for example, for example,

Slide 15 Fig. 1.7, p.14