General Physics I (aka PHYS 2013) P ROF . V ANCHURIN ( AKA V ITALY ) - PowerPoint PPT Presentation

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW General Physics I (aka PHYS 2013) P ROF . V ANCHURIN ( AKA V ITALY ) University of Minnesota, Duluth (aka UMD)

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW O UTLINE C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW S ECTION 1.1: T HE N ATURE OF P HYSICS ◮ Mathematics ◮ is the language of science: physics, astronomy, chemistry, engineering, geology, etc. ◮ very abstract math ideas find their way into science (e.g. complex numbers, differential geometry) ◮ It was conjectured that all of the mathematics has a physical realization somewhere (e.g. multiverse theories) ◮ Physics ◮ serves as a bridge (or foundation) to other sciences. ◮ one can never prove anything in physics, but math is also not as pure as seems (Godel’s theorems) ◮ it is however remarkable how successful the language of math is in describing the world around us. ◮ Think of physics as a toolbox of ideas which can be used in building scientific models in chemistry, biology, geology, astronomy, engineering, etc.

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW S ECTION 1.2: S OLVING P HYSICS P ROBLEMS ◮ Concepts ◮ in most disciplines the more material you can memorized the better your final grade will be. Not the case in physics. ◮ concepts is what you have to understand (actually there is only a single concept and almost everything follows) ◮ learning how to learn physics concepts will be your first and perhaps most difficult task. ◮ Problems ◮ the only way to evaluate if you really understand concepts is to solve problems. understanding solutions not enough. ◮ you might have hard time solving problems at first, but it is essential to learn how to solve problems on your own. ◮ keep track of how many problems you solved by yourself in each chapter (without anyone helping or googling)

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW S ECTION 1.3: S TANDARDS AND U NITS ◮ Units ◮ Physics is an experimental science and experiments involves measurements (e.g. time, length, mass). ◮ To express the results of measurements we use units. Units of length, units of time units of mass. ◮ There are some standard units just because historically we decided so (e.g. seconds, meters, kilograms). ◮ One can always convert from one system of units to another given a conversion dictionary. ◮ Time: measured in seconds, milliseconds, microseconds,... ◮ What is time and arrow of time is a deep philosophical question. We might discuss it a bit in the last day of classes in context of the second law of thermodynamics. ◮ Length: measured in meters, millimeters, micrometers, .... ◮ Despite of the fact that length and time appear to us very differently, there is a very deep connection (symmetry) between them. We might discuss is briefly when we discuss gravitation. ◮ Mass: measured in units of gram, milligram, microgram, ... ◮ Mass is also something very familiar to us in everyday life, but also has very deep properties connecting it so length and time. We might mention it briefly in connection to black-holes. ◮ Other units can be formed from seconds, meters and kilograms

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW S ECTION 1.4: C ONVERTING U NITS ◮ Dimension. ◮ Any physical quantity expressed in units of TIME, LENGTH or MASS is said to have dimensions of time, length or mass respectively. More generally one can have physical quantities which have mixed dimensions. For example if d has units of LENGTH and t has units of TIME, then quantity d v = (1) t has units of LENGTH/TIME. ◮ Evidently Eq. (1) has quantities with the same dimension (i.e. LENGTH/TIME) on both sides of the equation. This must be true for any equation that you write. Checking that the quantities on both sides of equation have the same dimension is a quick, but very important test that you could do whenever you setup a new equation. If the dimension is not the same than you are doing something wrong. Conversion. ◮ Sometimes you will need to convert from one system of units to another. This can always be done with the help of conversion dictionary. For the case of conversion from standard system of units to British system of units the dictionary is: 1 in = 2 . 54 cm (2) 1 pound = 4 . 448221615260 Newtons (3) ◮ If we are given a quantity in units of speed, then we can convert it from one system of units to another.

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW S ECTION 1.5: U NCERTAINTY AND S IGNIFICANT F IGURES Experimental Measurements. ◮ Measurements are always uncertain, but it was always hoped that by designing a better and better experiment we can improve the uncertainty without limits. It turned out not to be the case. ◮ There is a famous uncertainty principle of quantum mechanics, but you will only learn it next year in (PHYS 2021) if you decide to take it. ◮ From our point of view uncertainty is nothing but uncertainty in measurements. This (as well as significant figures) will be discussed in your lab course.

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW S ECTION 1.6: E STIMATES AND O RDER OF M AGNITUDE Theoretical Estimates. ◮ Similarly to uncertainties in experimental measurements, theoretical predictions are never exact. We always make simplifying assumption and thus the best we can hope for is an estimate for the physical quantities to be measured. ◮ A useful tool in such estimates is known as order-of-magnitude estimate (also know as outcome of “back-of-the-envelope calculations”). ◮ Such estimates are often done using the so-called dimensional analysis - i.e. just use the known quantities to form a quantity with the dimension of the quantity that you are looking for.

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW S ECTION 1.7: V ECTORS AND V ECTOR A DDITION Vectors. ◮ Some physical quantities are describe by a single real number. We call these quantities - scalar quantities or scalars. ◮ Other quantities also have a direction associated with them and thus are describe by three real numbers. � A = ( A x , A y , A z ) . (4) We call these quantities - vector quantities or vectors. There are also tensors etc. ◮ When dealing with vectors it is often useful to draw a picture: ◮ Vectors are nothing but straight arrows drawn from one point to another. Zero vector is just a vector of zero length - a point. ◮ Length of vectors is the magnitude of vectors. The longer the arrow the bigger the magnitude. ◮ It is assumed that vectors can be parallel transported around. If you attach beginning of vector � B to end of another vector � A then the vector � A + � B is a straight arrow from begging of vector � A to end of vector � B . Coordinates. ◮ The space around us does not have axis and labels, but we can imagine that these x, y and z axis or the coordinate system to be there. ◮ This makes it possible to talk about position of, for example, point particles using their coordinates - real numbers. ◮ Since one needs three real numbers to specify position it is a vector. Similarly, velocity, acceleration and force are all vectors.

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW S ECTION 1.8: C OMPONENTS OF V ECTORS ◮ Symmetry. You might complain that there is arbitrariness in how one chooses coordinate system or what components of the vector are and you would be right. It turns out that the physically observable quantities do not depend on the choice of coordinate systems and thus one can choose it to be whatever is more convenient. Moreover, this symmetry is an extremely deep property which gives rise to conservation laws that we will learn in this course. ◮ Magnitude. The length of vector or magnitude is a scalar quantity A = | � � A | = A (5) or in components � A 2 x + A 2 y + A 2 ( A x , A y , A z ) = z . (6) ◮ Direction. One can also find direction of vector using trigonometric identities. ◮ Addition. Two vectors can be added together to get a new vector C = � � A + � B (7) an in component form ( C x , C y , C z ) = ( A x , A y , A z ) + ( B x , B y , B z ) = ( A x + B x , A y + B y , A z + B z ) . (8)

C HAPTER 1 C HAPTER 2 C HAPTER 3 C HAPTER 4 R EVIEW S ECTION 1.9: U NIT V ECTORS ◮ Unit vectors is a vector (denoted with a hat) that has magnitude one. � | ˆ u 2 x + u 2 y + u 2 u | = z = 1 . (9) There are three unit vectors are so important that there are special letters reserved to denote these vectors ˆ i = ( 1 , 0 , 0 ) ˆ = ( 0 , 1 , 0 ) j ˆ = ( 0 , 0 , 1 ) . (10) k ◮ Multiplication / division by scalar. Any vector can be multiplied by a scalar to obtain another vector, � A = C � B . (11) In components from ( A x , A y , A z ) = C ( B x , B y , B z ) = ( CB x , CB y , CB z ) . (12) ◮ Components. Any vector can be written in components in two ways: j + A z ˆ � A = ( A x , A y , A z ) = A x ˆ i + A y ˆ k (13)