Units, Measurement, Dimension - Lecture Notes | PHY 231, Study notes of Physics

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PHY 231

PHYSICS 231

Lecture 1: Units, Measurement, Dimension

This could be the discovery of the century, depending

of course, on far it goes down”

PHY 231

Why?

Make No Mistake: Medical Errors Can Be Deadly Serious The American Hospital Association lists these as somecommon types of medication errors:•incomplete patient information•unavailable drug information•miscommunication of drug orders, which can involvepoor handwriting, confusion between drugs with similarnames, misuse of zeroes and decimal points, confusionof metric and other dosing units, and inappropriateabbreviations

PHY 231

What is a meter?

• Early 18

th

Century:

•Length of pendulum with half length of1s •Distance from N-pole to Equator viaParis /

7

• 1791: second was chosen and 1874 Alloy

was made

• 1889:more precise by using

Platinum/Iridium Alloy

• 1960:Using wavelength by using Krypton-

86 radiation

• 1983: distance traveled by light in vacuum

in 1/299792458 s

PHY 231

What is a second?

Originally 1/86400 of a mean solar day

1960: based on a tropical year

1967: 9192631770 periods of radiationcorresponding to the transition between twohyperfine states of the ground state of

133

Cesium

PHY 231

7

7 Standard Units: We will use them!!

Examples:Speed: m/s

Acceleration: m/s Force: kg·m/s

2

(N)

NIST: http://physics.nist.gov/cuu/index.html

Quantity

Name

unit

length

meter

m

mass

kilogram

kg

time

second

s

electrical Current

Ampere

A

temperature

Kelvin

K

amount of substance

mole

mol

Luminous intensity

candela

cd

Système Internationale (SI)

PHY 231

Dimensional Analysis

Dimension should be treated as algebraic quantities!

x=x

0

+(at

2

Correct dimensionally?

[m]=[m]+([m]/[s]

2

)[s]

2

… YES!

Think about unit conversions!

X,X

0

in ft. a in m/s

2

[ft]=[ft]+([m]/[s]

2

)[s]

2

1 m = 3.281 ft

[ft]=[ft]+([ft]/[s]

(^2)

)[s]

2

… YES!

GOOD WAY TO CHECK IN EXAMS & LIFE!!

PHY 231

Very large & very small numbers

=1E-15 femto (f)

=1E-12 pico (p)

=1E-9 nano (n)

=1E-6 micro (

μ

=1E-3 milli (m)

=1E-2 centi (c)

=1E-1 deci (d)

0

=1E+

1 =1E+1 deca (da)

2

=1E+2 hecto (h)

3

=1E+3 kilo (k)

6

=1E+6 mega (M)

9

=1E+9 giga (G)

12

=1E+12 tera (T)

PHY 231

Greek alphabet We will use some of those…

PHY 231

Circumference=

π

R=2·3.1415926... ·4.2 =

Significance & Uncertainty^ R=4.2 m

Calculator: 26.38937… mRight answer: 26 m.4.2 means that the true value liesbetween 4.1 and 4.3: 2

π

4.1=25.761…=26 m

2

π

4.3=27.0176…=27 m

so: Right Answer with error: 26±

The number of significant figures for a result of adivision or multiplication is the least accurate of thequantities being divided or multiplied.

PHY 231

Significance & Uncertainty

For addition and subtraction the number of decimal

places should be equal to the smallest number of

decimal places of any term in the sum:

NUMBER OF DECIMAL PLACES IS NOT

THE SAME AS THE NUMBER OF

SIGNIFICANT FIGURES!

0.0025: 2 significant figures 4 decimal placesScientific notation. For example 7·

7

or 7E+

PHY 231

3D geometrical objects

π

r

2 h

2

π

rh

cylinder

4/3 x

π

r

3

4

π

r

2

sphere

hlw

2hw+2lh+2wh

rectangle

length

3

6xlength

2

cube

volume

surface

object

PHY 231

Coordinate Systems

a

b

Cartesian Coordinates:(x,y)=(a,b)

r

θ

Plane polar coordinates:(r,

θ

a

b

b

a

r

/

)

tan(

2

(^2) =

=

θ

Frame transformation:

PHY 231

Be careful…

α

β

l^

h

h=l x sin

α

=l x cos

β

Check carefully which angle is given

PHY 231

Solving quadratic equations

a

ac

b

b

a x

c

bx

ax

2

4

0

0 2

2

−

±

−

≠ =

=

In general there are 2 solutions. In physics problems,One of them is often not realistic and is thrown out.