PHY121 Summer Session I, 2006

1. Instructor : Chiaki Yanagisawa PHY121 Summer Session I, 2006 • Most of information is available at: • http://nngroup.physics.sunysb.edu/~chiaki/PHY121-06. • 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 http://www.webassign.net. Your login username, institution • 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.

2. Chapter 1: Introduction • A physical quantity is measured in a unit which specifies the scale of the quantity. • SI units (Systèm International), also known as MKS A standard system of units for fundamental quantities of science an international committee agreed upon in 1960. Standards of Length, Mass and Time • Fundamental unit of length : meter (m) 1 m = 100 cm = 1,000 mm, 1 km = 1,000 m,… 1 inch = 2.54 cm = 0.0254 m, 1 foot = 30 cm = 0.30 m The meter was defined as the distance traveled by light in vacuum during a time interval of 1/299,792,458 seconds in 1980.

3. 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 = 0.454 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. Standards of Length, Mass and Time • Fundamental unit of time : second (s or sec) 1 sec = 1,000 msec = 1,000,000 msec,… 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.

4. 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 1025 Distance from Earth to nearest large galaxy (M31) 2 x 1022 Distance from Earth to closest star (Proxima Centauri) 4 x 1016 Distance for light to travel in one year (light year) 9 x 1015 Standards of Length, Mass and Time Distance from Earth to Sun (mean) 2 x 1011 Mean radius of Earth 6 x 106 Length of football field 9 x 101 Size of smallest dust particle 2 x 10-4 Size of cells in most living organism 2 x 10-5 Diameter of hydrogen atom 1 x 10-10 Diameter of atomic nucleus 1 x 10-14 Diameter of proton 1 x 10-15

5. 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 1052 Milky Way Galaxy 7 x 1041 Sun 2 x 1030 Standards of Length, Mass and Time Earth 6 x 1024 Human 7 x 101 Frog 1 x 10-1 Mosquito 1 x 10-5 Bacterium 1 x 10-15 Hydrogen atom 2 x 10-27 Electron 9 x 10-31

6. Other systems of units • cgs : length in cm, mass in g, time in s • area in cm2, volume in cm3, velocity in cm/s • U.S. customary : length in ft , mass in lb, time in s • area in ft2 , volume in ft3, velocity in ft/s Standards of Length, Mass and Time • Prefix 10-3 10-9 10-6 10-2 10-12 micro- (m) pico- (p) nano- (n) milli- (m) centi- (c) 103 109 106 101 1012 tera- (T) giga- (G) mega- (M) kilo- (k) deka- (da)

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

8. 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] = L2 (m2) Dimensional Analysis

9. 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/T2 • = [x]/[t]2 (m/s2) Dimensional Analysis

10. 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 +-0.1 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 +-0.1 cm. Therefore, the true value lies between • 16.2 cm and 16.4 cm. Uncertainty in Measurement 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

11. Area of a plate: length of sides 16.3+-0.1 cm, 4.5+-0.1 cm • The values of the area range between • (16.3-0.1 cm)(4.5-0.1 cm)= (16.2 cm)(4.4cm)=71.28 cm2 • =71 cm2and (16.3+0.1 cm)(4.5+0.1 cm)=75.44 cm2= • 75 cm2. • The mid-point between these two extreme values • is 73 cm2 with uncertainty of +-2 cm2 . • 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)

12. Two rules of thumb to determine the significant figures • 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. • Area of a plate: length of sides 16.3+-0.1 cm, 4.5+-0.1 cm • 16.3 x 4.5 = 73.35 = 73 (rounded to two significant figures). Uncertainty in Measurement (cont’d) 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

13. 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). • A sum of two numbers 123 and 5.35: • 123.xxx • + 5.35x • ------------ • 128.xxx • 123 + 5.35 = 128.35 = 128 zero decimal places two decimal places Uncertainty in Measurement (cont’d) zero decimal places

14. More complex example : 2.35 x 5.86/1.57 • - 2.35 x 5.89 = 13.842 = 13.8 • 13.8 / 1.57 = 8.7898 = 8.79 • - 5.89 / 1.57 = 3.7516 = 3.75 • 2.35 x 3.75 = 8.8125 = 8.81 • - 2.35 / 1.57 = 1.4968 = 1.50 • 1.50 x 5.89 = 8.835 = 8.84 Uncertainty in Measurement (cont’d) A lesson learned : Since the last significant digit is only one representative from a range of possible values, this amount of discrepancies is expected.

15. Since we use more than one unit for the same quantity, it is often necessary to convert one unit to another • Some typical unit conversions • 1 mile = 1,609 m = 1.609 km, 1 ft = 0.3048 m = 30.48 cm • 1 m = 39.37 in. = 3.281 ft, 1 in. = 0.0254 m = 2.54 cm • Example 1.4 • 28.0 m/s = ? mi/h Conversion of Units Step 1: Conversion from m/s to mi/s: Step 2: Conversion from mi/s to mi/h:

16. 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. • Examples • - 75 kg ~ 102 kg (~ means “is on the order of” or “is • approximately”) • - p = 3.1415…~1 (~3 for less crude estimate) Estimates and Order-of Magnitude

17. 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 Estimates and Order-of Magnitude Step 3: Number of gallons consumed per year

18. Example 1.8 : Number of galaxies in the Universe • Information given: Observable distance = 10 billion light year (1010 ly) • 14 galaxies in our local galaxy group • 2 million (2x106) ly between local groups • 1 ly = 9.5 x 1015 m Volume of the local group of galaxies: Number of galaxies per cubic ly: Estimates and Order-of Magnitude (cont’d) Volume of observable universe: Number of galaxies in the Universe:

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

20. Polar coordinate system A point in the two dimensional polar system is labeled with the coordinate (r, q) Coordinate Systems (cont’d)

21. sinq, cosq, tanq etc. Pythagorean theorem: hypotenuse side opposite q side adjacent q Trigonometry Inverse functions:

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

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