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Unformatted text preview: Physics 41 Lecture 1 Lecture 1: Dimensions; Kinematics in One Dimension Be sure you understand the following sections of the text, which will not be covered in detail in lecture: A Word About Vectors and Notation (Text 1.3). A vector is a quantity that has both a size and direction. Symbolically we denote vectors as letters with arrows over the top. For example, u1D45F is a vector quantity while u1D45F is a scalar quantity (just a number with no direction). We will discuss addition and subtraction of vectors in detail in Lecture 3. Section 1.8, especially significant figures, assessment and orders of magnitude and esti- mates. These are important skills that you can use in many situations. Goals of this lecture A discussion of the dimensions used in mechanics, and how to use dimensionality to check that a result is correct. Describing one dimensional motion with graphs of distance, velocity and acceleration vs. time. Use of the differential and integral relationships between acceleration, velocity and distance. 1.1 Variables, Dimensions and Units 1.1.1 Definitions of Standard Units Many units are defined in terms of quantum mechanical phenomena or in terms of fundamental constants of nature. For example: Time. One second is defined as the duration of 9,192,631,770 vibrations of a radiation emitted at a specific wavelength by a specified isotope of the cesium atom. Length is defined in terms of the speed of light in vacuum, combined with the time standard. One meter is defined as the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second. This is equivalent to saying that the speed of light in vacuum is exactly 299,792,458 m/s. 1.1.2 Dimensions in Mechanics In mechanics we can almost always get away with just three fundamental dimensions: mass, length and time, summarized in the table below. Variable Dimension Sample Units mass u1D45A M kg, g, lbs distance u1D451 L m, cm, feet time u1D461 T s, years Bold-face, upper-case letters denote the dimensions of mass, length and time: M , L and T . Non-boldface, lower-case letters denote the names of variables that have these dimensions; e.g. mass u1D45A , distance u1D451 , or time u1D461 . Other quantities that play an important r ole in mechanics can be written in terms of these three basic variables; For example acceleration has dimensions of length divided by time squared, L / T 2 . Square brackets [ ] around a variable denote the dimensions of that variable. For example: [ u1D44E ] = L / T 2 . 1 Last updated December 28, 2009 Physics 41 Lecture 1 1.1.3 Example: Using Dimensioned Variables in an Equation In this course we will frequency use Newtons second law of motion which in one dimension is: u1D439 = u1D45Au1D44E This states that in order to accelerate a mass u1D45A with acceleration u1D44E , you must provide a force u1D439 ....
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