Measurements in Physics The Language of Physics A unit is a particular physical quantity with which...

Measurements in Physics

The Language of Physics

A A unitunit is a particular physical quantity is a particular physical quantity with which other quantities of the same with which other quantities of the same kind are compared in order to express kind are compared in order to express their value. their value.

Measuring Measuring diameter of diameter of disk.disk.

A meter is an A meter is an established unit for established unit for measuring length.measuring length.

Based on definition, we Based on definition, we say the diameter is 0.12 say the diameter is 0.12 m or 12 centimeters.m or 12 centimeters.

SI System:SI System: The international system of The international system of units established by the International units established by the International Committee on Weights and Measures. Committee on Weights and Measures. Such units are based on strict Such units are based on strict definitions and are the only definitions and are the only officialofficial units for physical quantities.units for physical quantities.US Customary Units (USCU):US Customary Units (USCU): Older units Older units still in common use by the United still in common use by the United States, but definitions must be based States, but definitions must be based on SI units.on SI units.

One One metermeter is the length of path is the length of path traveled by a light wave in a vacuum traveled by a light wave in a vacuum in a time interval of 1/299,792,458 in a time interval of 1/299,792,458 seconds.seconds.

1 m1 m

1 second

299,792,458t

The The kilogramkilogram is the unit of is the unit of massmass - it is - it is equal to the mass of the international equal to the mass of the international prototype of the kilogram. prototype of the kilogram.

This standard is the only This standard is the only one that requires one that requires comparison to an artifact comparison to an artifact for its validity. A copy of for its validity. A copy of the standard is kept by the standard is kept by the International Bureau the International Bureau of Weights and Measures.of Weights and Measures.

The The secondsecond is the duration of 9 192 631 is the duration of 9 192 631 770 periods of the radiation 770 periods of the radiation corresponding to the transition between corresponding to the transition between the two hyperfine levels of the ground the two hyperfine levels of the ground state of the cesium 133 atom. state of the cesium 133 atom.

Cesium Fountain Cesium Fountain Atomic ClockAtomic Clock: The : The primary time and primary time and frequency frequency standard for the standard for the USA (NIST)USA (NIST)

Quantity Unit Symbol

Length Meter m

Mass Kilogram kg

Time Second S

Electric Current Ampere A

Temperature Kelvin K

Luminous Intensity Candela cd

Amount of Substance Mole mol

Website: Website: http://physics.nist.gov/cuu/index.htmlhttp://physics.nist.gov/cuu/index.html

Quantity SI unit USCS unit

Mass kilogram (kg) slug (slug)

Length meter (m) foot (ft)

Time second (s) second (s)

Force newton (N) pound (lb)

InIn mechanics mechanics we use only three we use only three fundamental quantities: fundamental quantities: mass, length, and mass, length, and timetime. An additional quantity, . An additional quantity, force,force, is is derived from these three.derived from these three.

King Henry Died By Drinking Chocolate Milk.

Prefix Symbol Multiplies Kilo K x 10 3

Hectoh x 10 2

Deka da x 10 Base Unit Deci d x 10 -1

Centi c x 10 –2

Milli m x 10 -3

1. 250 km = ________ m2. 53.2 dm = ________ cm3. 42.9 kg = ________ g4. 2,891 mm = ________ hm5. 68.3 milli-whaters= ________centi-

whatevers

Prefix Symbol Multiplies Giga G x10 9

Mega M x10 6

Micro µ x10 -6

Nano n x10 -9

250 Mg = 250 x 106 g 58 µm = 58 x 10 -6 m

1. Write down quantity to be converted.

2. Define each unit in terms of desired unit.

3. For each definition, form two conversion factors, one being the reciprocal of the other.

4. Multiply the quantity to be converted by those factors that will cancel all but the desired units.

Step 1: Write down Step 1: Write down quantity to be quantity to be converted.converted.

12 in.12 in.

Step 2. Define each unit in terms of desired unit.

1 in. = 2.54 1 in. = 2.54 cmcm

Step 3. For each definition, form two conversion factors, one being the reciprocal of the other.

1 in.

2.54 cm

2.54 cm

1 in

21 in. in.12 in. 4.72

2.54 cm cm

From Step 3. or 1 in.

2.54 cm2.54 cm

1 in

2.54 cm12 in. 30.5 cm

1 in.

Wrong Wrong ChoiceChoice!!

Step 4. Multiply by those factors that will cancel all but the desired units. Treat unit symbols algebraically.

Correct Correct Answer!Answer!

Step 3. For each definition, form 2 conversion factors, one being the reciprocal of the other.

1 mi = 5280 ft1 mi = 5280 ft

1 h = 3600 1 h = 3600 ss

1 mi 5280 ft or

5280 ft 1 mi

Step 3, shown here for clarity, can really Step 3, shown here for clarity, can really be done mentally and need not be be done mentally and need not be written down.written down.

Step 4. Choose Factors to cancel non-desired units.

mi 5280 ft 1 h60 88.0 m/s

h 1 mi 3600 s

Treating unit conversions algebraically helps to see if a definition is to be used as a multiplier or as a divider.

When writing numbers, zeros used When writing numbers, zeros used ONLY to help in locating the decimal ONLY to help in locating the decimal point are NOT significant—others are. point are NOT significant—others are. See examples.See examples.

0.0062 cm 0.0062 cm 2 significant 2 significant figuresfigures4.0500 cm 4.0500 cm 5 significant 5 significant

figuresfigures0.1061 cm 0.1061 cm 4 significant 4 significant figuresfigures50.0 cm 50.0 cm 3 significant 3 significant figuresfigures50,600 cm 50,600 cm 3 significant 3 significant figuresfigures

Rule 1. When approximate numbers are multiplied or divided, the number of significant digits in the final answer is the same as the number of significant digits in the least accurate of the factors.


245 N 6.97015 N/m

(3.22 m)(2.005 m)P ExamplExampl

e:e:

Least significant factor (45) has only Least significant factor (45) has only twotwo (2) digits so only (2) digits so only twotwo are justified in are justified in the answer.the answer.The appropriate The appropriate way to write the way to write the answer is:answer is:

P = 7.0 N/m2P = 7.0 N/m2

Rule 2. When approximate numbers are added or subtracted, the number of significant digits should equal the smallest number of decimal places of any term in the sum or difference.

Rule 2. When approximate numbers are added or subtracted, the number of significant digits should equal the smallest number of decimal places of any term in the sum or difference.Ex: Ex: 9.65 cm + 8.4 cm – 2.89 cm = 9.65 cm + 8.4 cm – 2.89 cm = 15.16 cm15.16 cmNote that the Note that the least preciseleast precise measure is measure is 8.4 cm8.4 cm. Thus, answer must be to . Thus, answer must be to nearest nearest tenthtenth of cm even though it of cm even though it requires 3 significant digits.requires 3 significant digits.The appropriate The appropriate way to write the way to write the answer is:answer is:

15.2 cm15.2 cm

Remember that significant figures Remember that significant figures apply to your apply to your reported resultreported result. . Rounding off your numbers in the Rounding off your numbers in the process can lead to errors.process can lead to errors.

Rule: Always retain at least one more significant figure in your calculations than the number you are entitled to report in the result.

Rule: Always retain at least one more significant figure in your calculations than the number you are entitled to report in the result.

With calculators, it is usually easier With calculators, it is usually easier to just keep all digits until you report to just keep all digits until you report the result.the result.

Rule 1.Rule 1. If the remainder If the remainder beyond the last beyond the last digitdigit toto be reportedbe reported is less than 5, drop is less than 5, drop the last digit.the last digit.Rule 2.Rule 2. If the remainder is greater than If the remainder is greater than 5, increase the final digit by 1.5, increase the final digit by 1.

Rule 3.Rule 3. To prevent rounding bias, if the To prevent rounding bias, if the remainder is exactly 5, then round the remainder is exactly 5, then round the last digit to the last digit to the closest even numberclosest even number..

Rule 1. If the remainder Rule 1. If the remainder beyond the last beyond the last digitdigit to be reported is less than 5, drop to be reported is less than 5, drop the last digit. the last digit.

Round the following to 3 significant Round the following to 3 significant figures:figures:

4.994994.99499

0.09400.09403395,63295,632

0.02030.020322

becomes becomes 4.994.99


becomes becomes 95,60095,600


Rule 2. If the remainder is greater Rule 2. If the remainder is greater than 5, increase the final digit by 1. than 5, increase the final digit by 1.


2.34522.3452

0.08750.08757723,650.023,650.0114.995024.99502



becomes becomes 23,70023,700


Rule 3. To prevent rounding bias, if the Rule 3. To prevent rounding bias, if the remainder is exactly 5, then round the remainder is exactly 5, then round the last digit to the last digit to the closest even numberclosest even number..


3.77503.7750000.024450.024450096,65096,650005.09505.095000


becomes becomes 0.02440.0244becomes becomes 96,60096,600


Quantity Unit Symbol

Length Meter m

Mass Kilogram kg

Time Second S

Electric Current Ampere A

Temperature Kelvin K

Luminous Intensity Candela cd

Amount of Substance

Mole mol

SUMMARYSUMMARY

1. Write down quantity to be converted.

2. Define each unit in terms of desired unit.

3. For each definition, form two conversion factors, one the reciprocal of the other.

4. Multiply the quantity to be converted by those factors that will cancel all but the desired units.


Rule 2. When approximate numbers are added or subtracted, the number of significant digits should equal the smallest number of decimal places of any term in the sum or difference.

Summary – Significant Summary – Significant DigitsDigits

Rule 1. If the remainder Rule 1. If the remainder beyond the last beyond the last digitdigit to be reported is less than 5, drop to be reported is less than 5, drop the last digitthe last digitRule 2. If the remainder is greater than Rule 2. If the remainder is greater than 5, increase the final digit by 1.5, increase the final digit by 1.

Rule 3. To prevent rounding bias, if the Rule 3. To prevent rounding bias, if the remainder is exactly 5, then round the remainder is exactly 5, then round the last digit to the last digit to the closest even numberclosest even number..

Measurements in Physics The Language of Physics A unit is a particular physical quantity with which...

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