Chapter 1 Measurement Fundamental Quantities in Physics Units & Conversion Three

Chapter 1 Measurement Fundamental Quantities in Physics Units & Conversion Three www.phwiki.com

Chapter 1 Measurement Fundamental Quantities in Physics Units & Conversion Three

Cabrera, Marc, Features Writer has reference to this Academic Journal, PHwiki organized this Journal Chapter 1 Measurement Fundamental Quantities in Physics Units & Conversion Three KEYS as long as Chapter 1 Fundamental quantities in physics (length, mass, time) Units (meters, kilograms, seconds ) Dimensional Analysis Force = kg meter/sec2 Power = Force x Velocity = kg m2/sec3 Three KEYS as long as Chapter 1 Fundamental quantities in physics (length, mass, time) Units (meters, kilograms, seconds ) Dimensional Analysis Significant figures in calculations 6.696 x 104 miles/hour 67,000 miles hour

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Three KEYS as long as Chapter 1 Fundamental quantities in physics (length, mass, time) Units (meters, kilograms, seconds ) Dimensional Analysis Significant figures in calculations Estimation (order of magnitude ~10 ) St in addition to ards in addition to units Length, mass, in addition to time = three fundamental quantities (“dimensions”) of physics. The SI (Système International) is the most widely used system of units. Meeting ISO st in addition to ards are m in addition to atory as long as some industries. Why In SI units, length is measured in meters, mass in kilograms, in addition to time in seconds. Converting Units A conversion factor is A ratio of units equal to 1 Used to convert between units Units obey same algebraic rules as variables & numbers

Converting Units km Converting Units km 1000 m = 1 km Multiplying by 1 doesn’t change the overall value, just the units. Converting Units km

Converting Units km Converting Units km cm Converting Units km cm

Unit consistency in addition to conversions An equation must be dimensionally consistent. Terms to be added or equated must always have the same units. (Be sure you’re adding “apples to apples.”) OK: 5 meters/sec x 10 hours =~ 2 x 102 km (distance/time) x (time) = distance Unit consistency in addition to conversions An equation must be dimensionally consistent. Terms to be added or equated must always have the same units. (Be sure you’re adding “apples to apples.”) OK: 5 meters/sec x 10 hours =~ 2 x 102 km 5 meters/sec x 10 hour x (3600 sec/hour) = 180,000 meters = 180 km = ~ 2 x 102 km Unit consistency in addition to conversions An equation must be dimensionally consistent. Terms to be added or equated must always have the same units. (Be sure you’re adding “apples to apples.”) OK: 5 meters/sec x 10 hours =~ 2 x 102 km NOT: 5 meters/sec x 10 kg = 50 Joules (velocity) x (mass) = (energy)

Unit prefixes Larger & smaller units as long as fundamental quantities. Learn these – in addition to prefixes like Mega, Tera, Pico, etc.! Skip Ahead to Slide 24 – Sig Fig Example Measurement & Uncertainty No measurement is exact; there is always some uncertainty due to limited instrument accuracy in addition to difficulty reading results. The precision – in addition to also uncertainty – of a measured quantity is indicated by its number of significant figures. Ex: 8.7 centimeters 2 sig figs Specific rules as long as significant figures exist In online homework, sig figs matter! In exams, sig figs matter!! Measurement & Uncertainty

Significant Figures Number of significant figures = number of “reliably known digits” in a number. Often possible to tell of significant figures by the way the number is written: 23.21 cm = four significant figures. 0.062 cm = two significant figures (initial zeroes don’t count). Significant Figures Significant figures are not decimal places 0.00356 has 5 decimal places, but just 3 significant figures Generally, round to the least number of significant figures of the given data 25 x 18 2 significant figures; 25 x 18975 still 2 Round up as long as 5+ (13.5 14, but 13.4 13) In general, trailing zeros are NOT significant In other words, 3000 may have 4 significant figures but usually 3000 will have only 1 significant figure! Numbers ending in zero are ambiguous. Does the last zero mean uncertainty to a factor of 10, or just 1 Significant Figures

Numbers ending in zero are ambiguous Is 20 cm precise to 10 cm, or 1 We need rules! 20 cm = one significant figure (trailing zeroes don’t count w/o decimal point) 20. cm = two significant figures (trailing zeroes DO count w/ decimal point) 20.0 cm = three significant figures Significant Figures Rules as long as Significant Figures When multiplying or dividing numbers, or using functions, result has as many sig figs as term with fewest (the least precise). ex: 11.3 cm x 6.8 cm = 77 cm. When adding or subtracting, answer is no more precise than least precise number used. ex: 1.213 + 2 = 3, not 3.213! Significant Figures Calculators will not give right of sig figs; usually give too many but sometimes give too few (especially if there are trailing zeroes after a decimal point). top image: result of 2.0/3.0 bottom image: result of 2.5 x 3.2

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Scientific Notation Scientific notation commonly used Uses powers of 10 to write large & small numbers Scientific Notation Scientific notation allows the number of significant figures to be clearly shown. Ex: cannot easily tell how many significant figures in “36,900”. Clearly 3.69 x 104 has three in addition to 3.690 x 104 has four! Remember trailing zeroes DO count with a decimal point (always in Scientific Notation!) Measurement & Uncertainty No measurement is exact; there is always some uncertainty due to limited instrument accuracy in addition to difficulty reading results. Photo illustrates this – it would be difficult to measure the width of this board more accurately than ± 1 mm.

Uncertainty in addition to significant figures Every measurement has uncertainty Ex: 8.7 cm (2 sig figs) “8” is (fairly) certain 8.6 8.8 8.71 8.69 Good practice – include uncertainty with every measurement! 8.7 0.1 meters Uncertainty in addition to significant figures Uncertainty should match measurement in the least precise digit: 8.7 0.1 centimeters 8.70 0.10 centimeters 8.709 0.034 centimeters 8 1 centimeters Not 8.7 +/- 0.034 cm Relative Uncertainty Relative uncertainty: a percentage, the ratio of uncertainty to measured value, multiplied by 100. ex. Measure a phone to be 8.8 ± 0.1 cm What is the relative uncertainty in this measurement

Solving problems in physics Step 3: Execute the Solution, in addition to EVALUATE your answer! Are the units right Is it the right order of magnitude Does it make SENSE Solving problems in physics Good problems to gauge your learning “Test your Underst in addition to ing” Questions throughout the book Conceptual “Clicker” questions linked online “Two dot” problems in the chapter Good problems to review be as long as e exams Checkpoints along the way ODD problems with answers in the back Exam reviews published online

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