1.2 Physical Quantities and Units

• The theories deal with the very small and the very fast.
• The behavior of small objects traveling at high speeds or experiencing a strong gravitational field is described by the combination of these two theories.
• Theoretical quantum mechanics is the best theory we have.
• The other theories are used whenever they will produce accurate results because of its mathematical complexity.
• We can do a lot of modern physics with the math used in this text.

• A friend tells you that he has learned something.

• If you don't know the details of the law, you can still infer that the information your friend has learned is in line with the laws of nature.
• If the information was a theory, you would be able to infer that it will be a generalization.

• You can learn about graphs.
• As the constants are adjusted, the shape of the curve changes.

• The distance from Earth to the Moon may seem large, but it is just a small fraction of the distances from Earth to other bodies.

• There are many objects and phenomena studied in physics.
• There are enough factors of 10 from the tiny sizes of sub-nuclear particles to the force by a jumping flea between Earth and the Sun.
• Giving numerical values for physical quantities and equations for physical principles allows us to understand nature more deeply.
• We must have accepted units in which to express them to comprehend these vast ranges.

• We define distance and time by specifying methods for measuring them, while we define average speed by stating that it is calculated as distance traveled divided by time of travel.

• The length of a race can be expressed in units of meters or kilometers.

• It would be difficult for scientists to express and compare measured values in a meaningful way without standardized units.

• The distances given in unknown units are useless.

• The metric system is also the standard system agreed upon by scientists and mathematicians.
• The French Systeme International is where the acronym "SI" comes from.

• The SI units are given in Table 1.1.
• The text uses non-SI units in a few applications, such as the measurement of blood pressure in millimeters of mercury.
• Non-SI units will be tied to SI units through conversions whenever they are discussed.

• Some physical quantities are more fundamental than others, and the most fundamental physical quantities can only be defined by the procedure used to measure them.
• The fundamental physical quantities are taken to be length, mass, time, and electric current.

• It used to be defined as 1/66,400 of a mean solar day.

• Cesium atoms can be made to vibrate in a way that can be observed and counted.
• The time required for 9,192,631,770 of these vibrations was redefined in 1967.
• All measurements are expressed in terms of fundamental units and can't be more accurate than the fundamental units themselves.

• An atomic clock such as this one uses the vibrations of cesium atoms to keep time to a precision of better than a microsecond per year.
• The second unit of time is based on these clocks.
• The distance from the equator to the North Pole was first defined in 1791.
• The distance between two engraved lines on a Platinumiridium bar was redefined in 1889.
• By 1960, it was possible to define the meter in terms of the wavelength of light, so it was again redefined as 1,650,763.73 wavelength of orange light.
• In 1983, the meter was given its current definition as the distance light travels in a vacuum.
• The speed of light is defined by this change.
• If the speed of light is measured with greater accuracy, the length of the meter will change.

• The distance light travels in a second in a vacuum is known as the meter.
• The distance traveled is determined by the speed at which it is traveled.

• The United States' National Institute of Standards and Technology, or NIST, located in Gaithersburg, Maryland outside of Washington D.C., is one of several locations around the world where replicas of the kilogram are kept.
• The standard mass could be compared to determine the determination of all other mass.
• Even though the cylinder was resistant tocorrosion, airborne contaminants were able to adhere to its surface, slightly changing its mass over time.
• The scientific community adopted a more stable definition of the kilogram in May.
• The kilogram is defined in terms of the second, the meter, and the constant, h, which is a quantum mechanical value that relates a photon's energy to its Frequency.

• When electricity and magnetism are present, the ampere and electric current will be introduced.
• The first modules in this textbook are about mechanics, fluids, heat, and waves.

• The units are categorized by factors of 10 in the metric system, making it convenient for scientific and engineering calculations.
• The table gives metric prefixes and symbols for various factors.

• The advantage of metric systems is that they only involve powers of 10.
• There are 100 centimeters in a meter, 1000 centimeters in a kilometer, and so on.
• The relationships in nonmetric systems are not as simple as in the U.S. customary units.
• The same unit can be used over large ranges of values simply by using an appropriate metric prefix.
• The tiny measure of nanometers is convenient in optical design, while distances in meters are suitable in construction.
• There is no need for new units in the metric system.

• The power in the metric system is represented by an order of magnitude.
• There are different orders of magnitude.
• The quantities that can be expressed as a product of a specific power are said to be of the same order of magnitude.

• The scale of a value can be estimated with the order of magnitude.
• The greatest accuracy and precision in measurement can be found in the fundamental units described in this chapter.
• Physicists feel that it would be more satisfying to base our standards of measurement on fundamental physical phenomena such as the speed of light, because there is an underlying substructure to matter.
• The standard of time is based on the oscillations of the cesium atom.

• The wavelength of light used to be the standard for length, but it has been replaced by the more precise measurement of the speed of light.
• If it becomes possible to measure the mass of atoms or a particular arrangement of atoms to greater precision than the kilogram standard, it may become possible to base mass measurements on the small scale.
• Current and charge are related to large-scale currents and forces between wires, but electrical phenomena on the small scale may someday allow us to base a unit of charge on the charge of electrons and protons.

• The wide range of examples of known lengths, mass, and times can be seen in Table 1.3.
• You can get a feel for the range of possible topics and numerical values by examining this table.

• The tiny plants swim in the ice.
• They can be as small as a few micrometers and as long as 2 millimeters in length.

• There are 2.4 billion light years away from Earth.
• Nature has a wide range of observable phenomena.

• Sometimes it is necessary to convert from one type of unit to another.
• If you are reading a European cookbook, some quantities may be expressed in units of liters and you need to convert them to cups.
• You are interested in how many miles you will be walking if you read walking directions from one location to another.
• You will need to convert units of feet to miles.

• An example of how to convert units is presented.
• We want to convert 80 meters to kilometers.

• List the units that you have and the units that you want to convert to.
• We want to convert the units in meters to kilometers.

• A conversion factor is a ratio that shows how many units are equal.
• There are 12 inches in 1 foot, 100 centimeters in 1 meter, 60 seconds in 1 minute, and so on.
• There are 1,000 meters in 1 kilometer.

• The unit conversion can now be set up.

• The unwanted m unit cancels and leaves only the desired km unit.
• This method can be used to convert between units.

• The average speed is calculated using the units.
• We can get the average speed into the units by using the correct conversion factor.
• The correct conversion factor cancels the unwanted unit and leaves the desired unit in its place.

• The distance traveled is divided by the average speed.

• Substitute the values for distance and time.

• The conversion factor that will cancel minutes and leave hours is 1.3.
• The conversion factor is.

• If you have properly canceled the units in the unit conversion, you can check your answer.
• The units will not cancel properly in the equation if you have written the unit conversion factor upside down.

• The problem asked us to find the average speed in units of km/ h and we have found them.

• The answer should have three significant figures because each of the values has three significant figures.
• The answer has three significant figures, so this is appropriate.
• The accuracy of the conversion factor is perfect because an hour is defined to be 60 minutes.

• If you travel 10 km in a third of an hour, you would travel three times that far in an hour.
• The answer seems reasonable.

• The average speed can be converted into meters per second.

• One of the conversion factors is needed to convert hours to seconds.

• If we had started with 0.500 km/min, we would have needed different conversion factors, but the answer would have been the same: 8.33 m/s.

• The answers in the worked example were given to three digits.
• The module Accuracy, Precision, and Significant Figures can help you answer these questions.

• There are many types of units that we are familiar with, but there are others that are not.
• Take note of the units that are not listed in the text.
• Think about the relationship between the unit and the SI units.

• The hummingbirds beat their wings 50 times per second.
• A scientist is measuring the time it takes for a hummingbird to fly.
• The metric prefix is related to the factor of 10.

• The scientist will use the fundamental unit of seconds to measure the time between movements.
• The scientist will need to measure in milliseconds or seconds because the wings beat so fast.

• One inch is equal to one liter.

• The derived unit of volume is probably created using the fundamental unit of length.
• The measurement of a liter is dependent on the measurement of a centimeter.

• A double-pan mechanical balance is used.
• An object with unknown mass is placed in one pan and an object with known mass is placed in the other.

• Metal cylinders of standard mass such as 1 gram, 10 grams, and 100 grams are known as the "known mass".
• Digital scales, which can measure the mass of an object more precisely, have replaced mechanical balances.
• Digital scales can measure the mass of an object up to the nearest thousandth of a gram, which is more than a mechanical balance can do.
• Science is based on observation and experiment.
• Let's say you are measuring the length of a computer paper.
• The paper in the packaging is not long.
• You measure the length of the paper three times.
• The measurement are very close to the correct value.
• If you had gotten a measurement of 12 inches, it wouldn't be very accurate.

• The paper measurements are an example.
• The range is the difference between the lowest and highest values of the measurement.
• The lowest value was in that case.
• The measured values deviated from each other.
• They were relatively precise because they didn't vary much in value.
• There would be significant variation from one measurement to another if the values had been 10.9, 11.1, and 11.9

• The paper example of the measurement is both accurate and precise, but in some cases it is not.
• An example of a gps system trying to locate the position of a restaurant in a city Think of the restaurant location as existing at the center of a bull's-eye target, and think of each gps attempt to locate the restaurant as a black dot.
• This shows a high accuracy measuring system.
• This shows a high accuracy measuring system.

• A restaurant is at the center of the bull's-eye.
• The black dots show the location of the restaurant.
• The dots are spread out far apart from one another, but they are close to the actual location of the restaurant, indicating high accuracy.
• The dots are close to one another, but far away from the actual location of the restaurant, indicating low accuracy.
• Uncertainty is a measure of how much your values deviate from what you expected.
• The uncertainty of your values will be high if your measurements are not very precise.
• Uncertainty can be seen as a caveat for your measured values.
• If you were asked to give the mileage on your car, you could say that it was 45,000 miles, plus or minus 500 miles.
• The uncertainty in your value is the plus or minus amount.
• It's possible that the actual mileage of your car could be as low as 44,500 miles or as high as 45,500 miles.
• There is some amount of uncertainty in all the measurements.
• We can say that the length of the paper is 11 in., plus or minus 0.2 in.
• The measurement result would be recorded as, because of the uncertainty in the measurement.

• There are other factors that affect the outcome.

• Factors that could contribute to the uncertainty are the smallest division on the ruler, the person using the ruler has bad eyesight, or one side of the paper is slightly longer than the other.
• Uncertainty in a measurement must be based on a careful consideration of all the factors that might contribute and their possible effects.

• In physics and many other real-world applications, uncertainty is a critical piece of information.
• You are caring for a sick child.
• You check the child's temperature with a thermometer if you suspect he or she has a high temperature.
• If the child's temperature reading was normal, the "true" temperature could be anywhere from a hypothermic to a dangerously high.
• The uncertainty of the thermometer would make it useless.

• It is possible to express uncertainty as a percent of the value.

• A store sells apples.
• You purchase four bags of apples and weigh them each time.

• The bag's expected value is 5 lbs.
• The uncertainty is about 0.4 lbs.

• The weight of the apple bag can be concluded.
• The uncertainty in the weight remained the same if the bag of apples were half as heavy.
• When calculating percent uncertainty, always remember to add the fraction by 100%.
• If you don't do this, you won't have a percent value.

• Anything calculated from measured quantities is uncertain.
• The area of a floor calculated from the measurement of its length and width has an uncertainty because of uncertainties.

• A coach bought a new stopwatch.

• Runners on the track coach's team clock 100m of sprints.
• The first- and second-place sprinters came in at the school's last track meet.

• The uncertainty in the stopwatch is too great to differentiate between sprint times.

• The precision of the measuring tool is an important factor in the accuracy of the measurement.
• A precise measuring tool can measure values in very small amounts.
• A ruler can measure length to the nearest millimeter, while a caliper can measure it to the nearest millimeter.
• The caliper can measure extremely small differences in length, which makes it a more precise measuring tool.
• The more precise the measuring tool is, the more accurate the measurement can be.

• We can only list as many digits as we originally measured, when we express measured values.
• If you use a standard ruler to measure the length of a stick, you can measure it to be.
• The measuring tool you used was not precise enough to measure a hundredth of a centimeter.
• The last digit in a measured value has been estimated by the person doing the measurement.

• To determine the number of significant digits in a value, start with the first measured value at the left and count the number of digits through the last digit written on the right.
• The measured value has significant figures.
• The figures show the precision of the tool used to measure the value.

• Special consideration is given to zeros.
• The zeros in 0.053 are not significant because they are only placekeepers.
• There are two significant figures.
• The zeros in 10.053 are not placekeepers but are significant.
• The style of writing numbers may affect the significance of the zeros in 1300.
• The number could be known to the last digit or it could be a placekeeper.
• 1300 could have two, three, or four significant figures.
• Zeros only serve as placekeepers.

• The number of significant figures should be determined.

• The number of significant digits in the final answer can't be greater than the number of significant digits in the least precise measured value.
• The rules for multiplication and division are different from the rules for addition and subtraction.

• The quantity with the least significant figures entering into the calculation should have the same number of significant figures.
• The area of a circle can be calculated using the radius.
• We can see how many significant figures the area has if the radius is only two.

• A calculator that has an eight-digit output will give you 1.11.

• The answer cannot contain more than the least precise measurement.
• If you buy 7.56 kilo of potatoes at a grocery store, you will get a scale with a precision of 0.01 kilo.
• The potatoes are measured by a scale with a precision of less than one kilo.
• You measure the potatoes on a bathroom scale with a precision of 0.1 kilogram.

• The least precise measurement is 13.7 kg.
• Our final answer must also be expressed to the 0.1 decimal place because this measurement is expressed to it.
• The answer is rounded to the tenths place, giving us 15.2 kilograms.

• Most numbers are assumed to have three significant figures.
• All worked examples use the same number of significant figures.
• An answer given to three digits is based on input good to at least three digits.
• The answer will have fewer significant figures if the input is less significant.
• The number of significant figures is reasonable for the situation.
• More accurate numbers are needed and more than three figures will be used in some topics.
• It does not affect the number of significant figures in a calculation if a number is exact.

• You can use the correct number of significant digits to express your answer.