01 lecture outline

Copyright © 2012 Pearson Education Inc – Modified 1/14 by Scott Hildereth, Chabot College.

PowerPoint® Lectures forUniversity Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman

Lecture 1

Units &Physical Quantities

Goals for Lecture 1• To learn three fundamental quantities of physics.

• To learn about the units of physical quantities.

• To study dimensional analysis.• To keep track of significant figures in calculations.

Introduction• The study of physics is important because physics is one of the most fundamental sciences, and one of the first applications of the pure study, mathematics, to practical situations.

• Physics is everywhere, appearing throughout our “day-to-day” experiences.

1.1 The nature of physics•Physics is an experimental science in which physicists seek patterns that relate the phenomena of nature.

•Physics: the study of the fundamental laws of nature.

These laws can be expressed as mathematical equations. (e.g., F = m a)

Most physical quantities have units, which must match on both sides of an equation.

Much complexity can arise from even relatively simple physical laws.

Quantitative vs Qualitative (Measurements vs Descriptions)

•Scientists do not use descriptions to make

observations as these would most likely cause disagreements.

•“How large is large?” or “How small is small?”

•Instead, sizes are specified using a number and a standard

unit such as the metre.

Physical Quantities

What is a Physical Quantity???Definition:Definition:

A physical quantity is one that can be measured and that consist of a numerical magnitude and a unit.

Examples include length, volume, time and temperature.

1.2 Standards and units

With a few exceptions, all physical quantities have units. Examples:Mass - kilograms (kg)Speed - meters per second (m/s)Pressure - pascals (P)

Energy - joules (J)Electric Potential - volts (V) Rather surprisingly, the units of almost all physical quantities can be expressed as combinations of only the units for mass, length, and time, i.e., kilograms, meters, and seconds. A few physical quantities are pure numbers that have no associated units

1.2 Standards and units• Length, mass, and time = three

fundamental quantities (“dimensions”) of physics.

• The SI (Système International) is the most widely used system of units.

• In SI units, length is measured in meters, mass in kilograms, and time in seconds.

Unit Conversions

1 in = 2.54 cm 1 cm = 0.3937 in1 mi = 1.609 km 1 km = 0.621 mi1 mph = 0.447 m/s1 m/s = 2.24 mph

Base Quantity

There are 7 base quantities.All the other quantities (derived quantities) can be worked out from the 7 base quantities.Base Quantities1. Length2. Mass3. Time4. Temperature5. Electric current6. Luminous intensity7. Amount of substance

Why are these quantities called base quantities?

Base quantities are physical quantities that cannot be defined in

terms of other base quantitiesBase Base

quantityquantitySymbolSymbol SI unitSI unit Symbol of Symbol of

SI unitSI unitLengthLength ll metremetre mm

MassMass mm kilogramkilogram kgkg

TimeTime tt secondsecond ss

TemperaturTemperaturee

TT KelvinKelvin KK

Electric Electric currentcurrent

II ampereampere AA

1.3 Unit Conversions

• Example 1.1 Express the speed limit of 763.0 miles/hour in meters/second.

• Example 1.2 Express the volume of 1.84 cubic inches in cubic centimeters and in cubic meters.

Standards and units• Base units are set for length, time, and mass.

• Unit prefixes size the unit to fit the situation.

1.3 Unit prefixes•Table 1.1 shows some larger and smaller units for the fundamental quantities.

Derive Quantities & UnitsAll other quantities are derived from this base quantities15

Derived quantity

Relation with base and derived quantities

Symbol for unit

Special name

volume length × width × height

m3

density mass ÷ volume kg m3

Speed distance ÷ time m s-1

acceleration

change in velocity ÷ time

m s-2

force mass × acceleration

kg m s-2 (N) newton (N)

pressure force ÷ area kg m-1 s-2 (N m-2)

pascal (Pa)

work force × distance kg m2 s-2 (N m)

joule (J)

power work ÷ time kg m2 s-3 (J s-1)

watt (W)

Unit consistency and conversions• An equation must be dimensionally consistent (be sure you’re “adding apples to apples”).

• “Have no naked numbers” (always use units in calculations).

• Refer to Example 1.1 (page 7) and Example 1.2 (page 8).

1.4 Dimensional Analysis[L] = length [M] = mass [T] = time

Is the following equation dimensionally correct?

221 vtx

TLTTLL 2

No

1.5 Measurement & Uncertainty

No measurement is exact; there is always some uncertainty due to limited instrument accuracy and difficulty reading results.

The precision – and also uncertainty -

of a measured quantity is

indicated by its number of significant

figures.Ex: 8.7 centimeters

2 sig figs

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).

Numbers ending in zero are ambiguous. Does the last zero mean uncertainty to a factor of 10, or just 1?

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 for 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!

1.6 Scientific Notation

•Scientific notation is commonly used in physics; it 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;

and 3.690 x 104 has four.

1-7 Order of Magnitude: Rapid Estimating

Quick way to estimate calculated quantity:

• round off all numbers in a calculation to one significant figure and then calculate. • result should be right order of magnitude• expressed by rounding off to nearest power of 10

• 104 meters• 108 light years

Order of Magnitude: Rapid Estimating

Example: Volume of a lake

Estimate how much water there is in a particular lake, which is roughly circular, about 1 km across, and you guess it has an average depth of about 10 m.



Volume = x r2 x depth= ~ 3 x 500 x 500 x 10= ~75 x 105

= ~ 100 x 105

= ~ 107 cubic meters



Volume = x r2 x depth= 7,853,981.634 cu. m

~ 107 cubic meters

Solving problems in physics

• The textbook offers a systematic problem-solving strategy with techniques for setting up and solving problems efficiently and accurately.


• Step 1: Identify relevant concepts, variables, what is known, what is needed, what is missing.


• Step 2: Set up the Problem – MAKE a SKETCH, label it, act it out, model it, decide what equations might apply. What units should the answer have? What value?


• Step 3: Execute the Solution, and EVALUATE your answer! Are the units right? Is it the right order of magnitude? Does it make SENSE?

01 lecture outline

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