PHY121 Summer Session I, 2006 Most of information is available at: It will be frequently updated. Homework assignments for each chapter due a week later (normally) and are delivered through WebAssign. Once the deadline has passed you cannot input answers on WebAssign. To gain access to WebAssign, you need to obtain access code and go to Your login username, institutionhttp:// name and password are: initial of your first name plus last name (such as cyanagisawa), sunysb, and the same as your username, respectively. In addition to homework assignments, there is a reading requirement of each chapter, which is very important. The lab session will start next Monday (June 5), for the first class go to A-117 at Physics Building. Your TAs will divide each group into two classes in alphabetic order. Instructor : Chiaki Yanagisawa

Chapter 1: Introduction Standards of Length, Mass and Time  A physical quantity is measured in a unit which specifies the scale of the quantity. Fundamental unit of length : meter (m) 1 m = 100 cm = 1,000 mm, 1 km = 1,000 m,… 1 inch = 2.54 cm = m, 1 foot = 30 cm = 0.30 m SI units (Systèm International), also known as MKS A standard system of units for fundamental quantities of science an international committee agreed upon in The meter was defined as the distance traveled by light in vacuum during a time interval of 1/299,792,458 seconds in 1980.

 A physical quantity is measured in a unit which specifies the scale of the quantity (cont’d) Fundamental unit of mass : kilogram (kg) 1 kg = 1,000 g, 1 g = 1,000 mg, 1 ton = 1,000 kg 1 pound = kg = 454 g, 1 ounce = 28.3 g The kilogram is defined as the mass of a specific platinum iridium alloy cylinder kept at the International Bureau of Weights and Measures in France. Fundamental unit of time : second (s or sec) 1 sec = 1,000 msec = 1,000,000  sec,… 1 hour = 60 min = 3,600 sec, 24 hours = 1 day The second is defined as 9,192,631,700 times the period of oscillation of radiation from cesium atom. Standards of Length, Mass and Time

 A physical quantity is measured in a unit which specifies the scale of the quantity (cont’d) Scale of some measured lengths in m Distance from Earth to most remote normal galaxies 4 x Distance from Earth to nearest large galaxy (M31) 2 x Distance from Earth to closest star (Proxima Centauri) 4 x Distance for light to travel in one year (light year) 9 x Distance from Earth to Sun (mean) 2 x Mean radius of Earth 6 x 10 6 Length of football field 9 x 10 1 Size of smallest dust particle 2 x Size of cells in most living organism 2 x Diameter of hydrogen atom 1 x Diameter of atomic nucleus 1 x Diameter of proton 1 x Standards of Length, Mass and Time

 A physical quantity is measured in a unit which specifies the scale of the quantity (cont’d) Scale of some measured masses in kg Observable Universe 1 x Milky Way Galaxy 7 x Sun 2 x Earth 6 x Human 7 x 10 1 Frog 1 x Mosquito 1 x Bacterium 1 x Hydrogen atom 2 x Electron 9 x Standards of Length, Mass and Time

 Other systems of units cgs : length in cm, mass in g, time in s area in cm 2, volume in cm 3, velocity in cm/s U.S. customary : length in ft, mass in lb, time in s area in ft 2, volume in ft 3, velocity in ft/s Standards of Length, Mass and Time  Prefix pico- (p)nano- (n) micro-  milli- (m)centi- (c) tera- (T)giga- (G)mega- (M)kilo- (k)deka- (da)

The Building Blocks of Matter  History of model of atoms electrons e - nucleus (protons and neutrons) Old view Modern view nucleus quarks proton Semi-modern view

Dimensional Analysis  In physics, the word dimension denotes the physical nature of a quantity The distance can be measured in feet, meters,… (different unit), which are different ways of expressing the dimension of length. The symbols that specify the dimensions of length, mass and time are L, M, and T. dimension of velocity [v] = L/T (m/s) dimension of area [A] = L 2 (m 2 )

Dimensional Analysis  In physics, it is often necessary either to derive a mathematical expression or equation or to check its correctness. A useful procedure for this is called dimensional analysis. Dimensions can be treated as algebraic quantities: dimension of distance [x] = L (m) dimension of velocity [v] = [x]/[t] = L/T (m/s) dimension of acceleration [a] = [v]/[t] = (L/T)/T = L/T 2 = [x]/[t] 2 (m/s 2 )

Uncertainty in Measurement  In physics, often laws in form of mathematics are tested by experiments. No physical quantity can be determined with complete accuracy. Accuracy of measurement depends on the sensitivity of the apparatus, the skill of the person conducting the measurement, and the number of times the measurement is repeated. For example, assume the accuracy of measuring length of a rectangular plate is cm. If a side is measured to be 16.3 cm, it is said that the length of the side is measured to be 16.3 cm cm. Therefore, the true value lies between 16.2 cm and 16.4 cm. Significant figure : a reliably known digit In the example above the digits 16.3 are reliably known i.e. three significant digits with known uncertainty

Uncertainty in Measurement (cont’d) Area of a plate: length of sides cm, cm The values of the area range between ( cm)( cm)= (16.2 cm)(4.4cm)=71.28 cm 2 =71 cm 2 and ( cm)( cm)=75.44 cm 2 = 75 cm 2. The mid-point between these two extreme values is 73 cm 2 with uncertainty of +-2 cm 2. Two significant figures! (Note that 0.1 has only one significant figure as 0 is simply a decimal point indicator.)

Uncertainty in Measurement (cont’d) 1)In multiplying (dividing) two or more quantities, the number of significant figures in the final product (quotient) is the same as the number of significant figures in the least accurate of the factors being combined, where least accurate means having the lowest number of significant figures.  Two rules of thumb to determine the significant figures Area of a plate: length of sides cm, cm 16.3 x 4.5 = = 73 (rounded to two significant figures). three (two) significant figures To get the final number of significant digit, it is necessary to do some rounding: If the last digit dropped is less than 5, simply drop the digit. If it is greater than or equal to 5, raise the last retained digit by one

Uncertainty in Measurement (cont’d) A sum of two numbers 123 and 5.35: 123.xxx x xxx = = 128 zero decimal places two decimal places zero decimal places 2)When numbers are added (subtracted), the number of decimal places in the result should equal the smallest number of decimal places of any term in the sum (difference).

Uncertainty in Measurement (cont’d) More complex example : 2.35 x 5.86/ x 5.89 = = / 1.57 = = / 1.57 = = x 3.75 = = / 1.57 = = x 5.89 = = 8.84 A lesson learned : Since the last significant digit is only one representative from a range of possible values, this amount of discrepancies is expected.

Conversion of Units Some typical unit conversions 1 mile = 1,609 m = km, 1 ft = m = cm 1 m = in. = ft, 1 in. = m = 2.54 cm Example m/s = ? mi/h Step 1: Conversion from m/s to mi/s: Step 2: Conversion from mi/s to mi/h:  Since we use more than one unit for the same quantity, it is often necessary to convert one unit to another

Estimates and Order-of Magnitude Examples - 75 kg ~ 10 2 kg (~ means “is on the order of” or “is approximately”) -  = …~1 (~3 for less crude estimate)  For many problems, knowing the approximate value of a quantity within a factor of 10 or so is quite useful. This approximate value is called an order-of-magnitude estimate.

Estimates and Order-of Magnitude Example 1.6 : How much gasoline do we use? Estimate the number of gallons of gasoline used by all cars in the U.S. each year Step 1: Number of cars Step 2: Number of gallons used by a car per year Step 3: Number of gallons consumed per year

Estimates and Order-of Magnitude (cont’d) Example 1.8 : Number of galaxies in the Universe Information given: Observable distance = 10 billion light year (10 10 ly) 14 galaxies in our local galaxy group 2 million (2x10 6 ) ly between local groups 1 ly = 9.5 x m Volume of the local group of galaxies: Number of galaxies per cubic ly: Volume of observable universe: Number of galaxies in the Universe:

Coordinate Systems Cartesian coordinate system A point in the two dimensional Cartesian system is labeled with the coordinate (x,y)  Locations in space need to be specified by a coordinate system

Coordinate Systems (cont’d) Polar coordinate system A point in the two dimensional polar system is labeled with the coordinate (r 

Trigonometry sin , cos , tan  etc. hypotenuse side opposite  side adjacent  Pythagorean theorem: Inverse functions:

Trigonometry (cont’d) Example 1.9 : Cartesian and polar coordinates Cartesian to polar: (x, y)=(-3.50,-2.50) m Polar to Cartesian: (r  )=(5.00 m, 37.0 o )

Trigonometry (cont’d) Example 1.10 : How high is the building What is the height of the building? What is the distance to the roof top? r, hypotenuse