PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Chapter 1: Models measurements and vectorsMetric(SI) PrefixesSI Base Quantities and UnitsMassLengthSlide 15TimeSlide 17Vectors and vector additionSlide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Vector MultiplicationExamples of vector quantitiesExamples of scalar quantitiesReference frame (system) or system of coordinatesReference frame and unit vectors on a planeVector propertiesOperations on vectorsRadius-vectorSpecifying a VectorPhysical quantitiesUnits SIConversion of unitsConversion of units (2nd example)Dimensional analysisRules for significant figuresSlide 50PHYSICS 201 (sections 521-525) Instructor: Hans Schuessler Occasionally : AlexandreKolomenskihttp://sibor.physics.tamu.edu/teaching/phys201/Contact information e-mail: [email protected]([email protected]) Office : 442 Mitchell Physics Building. Office hours: Thursdays 12:30 pm – 1:30 pmTel. 845-5455•College Physics with Mastering Physics (9th Ed.) by Young•PHYS 201 Lab Manual (12th Ed. Hayden-McNeil)and occasional in class quizzes (87Make your own cheat sheet 1 page for the classAbū Alī al- asan ibn al- asan ʿ Ḥ Ḥibn al-Haytham (965 in Basra – c. 1040 in Cairo) was a Muslim, Persian or Arab scientist and polymath. He is frequently referred to as Ibn al-Haytham, and sometimes as al-Basri (Arabic: يرصب لااا ), after his birthplace in the city of Basra.[12] Alhazen made significant contributions to the principles of optics, as well as to physics, astronomy, mathematics, ophthalmology, philosophy, visual perception, and to the scientific methodChapter 1: Models measurements and vectorsMetric(SI) PrefixesSI Base Quantities and Units1kg = mass of the platinum-iridium cylinder in Paris 1u = 1.6605 10-27kg ( unified atomic mass unit) MassLength1m  10-7 of the distance from the equator to the pole1m = length of the path traveled by light in vacuum during the time interval of 1/299,792,458 of a secondTime1s = 1/24*60*60 day=1/86400 day 1s = time required for 9,192,631,720 periods of radiation of the Cs-atomVectors and vector additionScalar product Vector product Vector MultiplicationCABBAABBAsincoskBABAjBABAiBABABBBAAAkjiBAxyyxzxxzyzzyzyxzyx)()()( Examples of vector quantities1. Displacement2. Velocity3. Acceleration 4. Force?Examples of scalar quantities1. Distance2. Speed3. Time 4. Mass?Reference frame (system) or system of coordinatesAlmost any problem in mechanics starts with selection of the reference system.To determine the location of an object we provide its position in respect to some other object or point that we select as an origin.Reference frame and unit vectors on a planeVector properties222zyxAAAA Vector A has componentsIt has a magnitude(absolute value) for 2D case },,{zyxAAA},{yxAA22yxAAA Operations on vectors1. Sum and subtract2. Multiply by a numberYou can do this by components!For components it works just as with numbers!Radius-vectorThe tale of this vector is always in the origin of the reference frame. Describes position of a point on a plane (in 2D, 2 numbers: {x,y})or in space (in 3D, 3 numbers, {x,y,z})Specifying a Vector•A vector can be presented as a sum of its components! •Two equivalent ways: –Components Vx and Vy–Magnitude V and angle •Switch back and forth–Magnitude of V |V| = (vx2 + vy2)½(Pythagorean Theorem)–Tan = vy /vxEither method is fine, but you should pick which iseasiest, and be able to useboth.Physical quantities1. Always have some units!2. From relationships between these quantities one can derive new unitsUnits SIDisplacement, distance: 1 meter 1mVelocity, speed: 1 meter/second 1m/sAcceleration: 1 meter/second2 1m/s2Conversion of units•We would like to find how many meters in 20 miles, how do we do this?•We go to the pages in the end of the textbook, Appendix E “Unit conversion Factors” and use the formula1 mile=1.609 kmnow we know 1km=1000 m then20 mi=20x1.609x1000 m=32180 mConversion of units (2nd example)We would like to know, what will be 18 km/h in m/s?18 km/h=18x1000m/(60x60s)=5 m/sDimensional analysis•You have three equations with distance x, speed V, time t and acceleration a, which of them can be correct?22atx 22Vtx aVx22Rules for significant figures(1)When numbers are multiplied or divided, the number of significant figures in the final answer equals the smallest number of significant figures in any of the original factors.(2) When numbers are added or subtracted, the last significant figure in the answer occurs in the last column (counting from left to right) containing a number that results from a combination of digits that are all significant.Indication of significant figures using scientific notation: decimal number with one digit to the left of the decimal point, multiplied by the appropriate power of