general physics I, lec 1 1 Chapter (1,2)

general physics I, lec 1 2 Physical quantities (in mechanics) Basic quantities : in mechanics the three fundamental quantities are length(L) mass (M) time (t) Derived quantities : all other physical quantities in mechanics can be expressed in term of basic quantities Area Volume Velocity Acceleration Force Momentum Work …..

general physics I, lec 1 3 Systems of Units SI units ( International System of Units ): length: meter (m) mass: kilogram (kg) time: second (s) This system is also referred to as the mks system for meter-kilogram-second. Gaussian units length: centimeter (cm) mass: gram (g) time: second (s) This system is also referred to as the cgs system for centimeter-gram-second. British engineering system: length: foot (ft) mass: slug time: second (s)

general physics I, lec 1 4 Mass The SI unit of mass is the Kilogram, which is defined as the mass of a specific platinum-iridium alloy cylinder. Time The SI unit of time is the Second, which is the time required for a cesium-133 atom to undergo vibrations. Length The SI unit of length is Meter, which is the distance traveled by light is vacuum during a time of 1/ second.

general physics I, lec 1 5 Dimension [L]=L [M]=M [T]=T Quantity Length Mass time [A] = L 2 area [V]=L 3 volume [v]= L/Tvelocity [a] = L/T 2 [f]=M L/T 2 Acceleration force Dimensional Analysis Definition: The Dimension is the qualitative nature of a physical quantity (length, mass, time). brackets [ ] denote the dimension or units of a physical quantity:

general physics I, lec 1 6 Idea: Dimensional analysis can be used to derive or check formulas by treating dimensions as algebraic quantities. Quantities can be added or subtracted only if they have the same dimensions, and quantities on two sides of an equation must have the same dimensions Example(1) Using the dimensional analysis check that this equation x = ½ at 2 is correct, where x is the distance, a is the acceleration and t is the time. left hand side right hand side This equation is correct because the dimension of the left and right side of the equation have the same dimensions. Solution

general physics I, lec 1 7 Example(2) Suppose that the acceleration of a particle moving in circle of radius r with uniform velocity v is proportional to the r n and v m. Use the dimensional analysis to determine the power n and m. The left hand side Therefore or Solution Let us assume a is represented in this expression a = k r n v m Where k is the proportionality constant of dimensionless unit. The right hand side [ a] = L/T 2

general physics I, lec 1 8 Hence n+m=1 and m=2 Therefore n =-1 and the acceleration a is a = k r -1 v 2 Problems: 1. Show that the expression x = vt +1/2 at 2 is dimensionally correct, where x is coordinate and has unit of length, v is velocity, a is acceleration and t is the time. 2. Show that the period T of a simple pendulum is measured in time unit given by

general physics I, lec 1 9 Coordinate Systems and Frames of Reference The location of a point on a line can be described by one coordinate; a point on a plane can be described by two coordinates; a point in a three dimensional volume can be described by three coordinates. In general, the number of coordinates equals the number of dimensions. A coordinate system consists of: 1. a fixed reference point (origin) 2. a set of axes with specified directions and scales 3. instructions that specify how to label a point in space relative to the origin and axes

general physics I, lec 1 10 For Example: (rectangular coordinate system): (x,y) Cartesian coordinate system Plane polar coordinates:

general physics I, lec 1 11 The relation between coordinates Furthermore, it follows that Problem: A point is located in polar coordinate system by the coordinate and. Find the x and y coordinates of this point, assuming the two coordinate systems have the same origin.

general physics I, lec 1 12 Example (3): The Cartesian coordinates of a point are given by (x,y)= (-3.5,-2.5) meter. Find the polar coordinates of this point. Solution: Note that you must use the signs of x and y to find that is in the third quadrant of coordinate system. That is not 36

general physics I, lec 1 13 Scalars and Vectors Scalars have magnitude only. Length, time, mass, speed and volume are examples of scalars. Vectors have magnitude and direction. The magnitude of is written | | v Position, displacement, velocity, acceleration and force are examples of vector quantities. Vectors have the following properties : 1. Vectors are equal if they have the same magnitude and direction.

general physics I, lec Multiplication or division of a vector by a scalar results in a vector for which (a) only the magnitude changes if the scalar is positive (b) the magnitude changes and the direction is reversed if the scalar is negative. 2. Vectors must have the same units in order for them to be added or subtracted. 3. The negative of a vector has the same magnitude but opposite direction.

general physics I, lec Vector Addition: The sum of two vectors, A and B, is a vector C, which is obtained by placing the initial point of B on the final point of A, and then drawing a line from the initial point of A to the final point of B, as illustrated in figure C = A + B 6. Subtraction of a vector is defined by adding a negative vector:

general physics I, lec The projections of a vector along the axes of a rectangular coordinate system are called the components of the vector. The components of a vector completely define the vector.

general physics I, lec 1 17 Problem: