Physics: Physical Quantities and Vectors PDF

PHYSICAL QUANTITIES AND VECTORS Zeroes between nonzero digits are significant. Physics - one of the main branches of Zeroes before nonzero digits are not science which ai...

PHYSICAL QUANTITIES AND VECTORS Zeroes between nonzero digits are significant. Physics - one of the main branches of Zeroes before nonzero digits are not science which aims to gain greater significant. understanding of the nature of matter and Zeroes after nonzero digits are not energy. significant if no decimal point is Modern physics - started in 1900 with Max present. Planck’s discovery of blackbody radiation. Zeroes after nonzero digits are significant if a decimal point is Classical physics - all discoveries, present principles, and inventions prior to 1900 Unit Conversion The Measuring Process The simplest way to convert one unit to Measurement – process of comparing another is to form a conversion ratio (equal something with a standard. to one) with the desired unit on the Metric System numerator and the unit to be converted at mks- meter, kilogram, second the denominator. cgs- centimeter, gram, second Accuracy versus Precision English system Accuracy - refers to the closeness of a fps- foot, pound, and second. measured value to the expected or true value of a physical quantity. Precision - represents how close or consistent the independent measurements of the same quantity are to one another. Scientific Notation and Significant Figures Scientific Notation – a convenient and widely used method of expressing large and small numbers. SI Prefixes It is expressed in the form N x 10n Significant Figures - number of digits which contribute to the accuracy and precision of certain measurements. Rules to determine which digits are significant. Nonzero digits are significant  The word north or south is written after the measure of the angle followed by the phrase “of east” or “of west”. Vector Addition Resultant Vector - the sum of two or more vector quantities The notation R – usually used to represent the resultant. The two properties of vector addition are Working with Directions commutative and associative properties. Vectors Vector addition is commutative Quantities in physics may either be scalar A+B=B+A or vector. Vector addition is also associative Scalar quantities - can be described (A+B)+C=A+(B+C) completely by their magnitudes and appropriate units. Methods of Vector Addition Ex. mass, temperature, speed, and time. The graphical method is subdivided into Vector quantities - completely described by 1. Parallelogram their magnitudes, appropriate units and 2. polygons methods. direction. The analytical method is subdivided into Ex. force, displacement, velocity and 1. using the law of sines and cosines acceleration. 2. component methods. Vector Representation and Direction Solving Vector using the Law of Sines and A vector quantity could be represented by Cosines an arrow. Law of Sines The symbol for vector quantities is an For a triangle with sides a,b,c and opposite italicized capital letter in boldface or with an angles A,B and C, the law is given by: arrow on top. The direction of a vector is the acute angle it makes with the east-west line.  Vector Multiplication Three ways of vector multiplication Product of a vector and a scalar Dot product of two vectors Law of Cosines Cross product of two vectors. Product of a Vector and a Scalar The product of k and V, written as kV, is a vector. Typical examples where a vector quantity is multiplied to a scalar quantity are momentum and force. Dot Product Scalar Product - the dot product of two vectors A and B The dot product is written and defined as Vector Subtraction A ∙ B = AB cos ∅ The negative of a vector V, written as –V, is a vector equal in magnitude to V but in the opposite direction. To subtract vector B from vector A, we simply add the negative of B to A. A – B = A + (-B) Example 1 Find A - B for the following cases: (a)A = 6 units,east and B= 4 units, west; and (b)A= The dot product of two nonzero vectors may 7.0m,60° north of east and B= 5.0 m,east. be positive, negative, or zero, depending on the angle between them Since the dot product of two vectors is a Example: Suppose the student went back scalar, then the dot product is from school to his house commutative, that is, A ∙ 𝐵 = 𝐵 ∙ A Note that the magnitude of displacement Work - the dot product of force F and does not necessarily equal to distance. displacement d. It is a scalar quantity Speed versus Velocity whose unit is the joule (J), which is equal to 1 newton-meter (N∙m). Speed - the distance traveled by a body in a given time. It is a scalar quantity. Kinematic Equations of Motion Velocity - the time rate of change of Kinematics - describes motion in terms of position. It is the displacement of a body in displacement, velocity, and acceleration. a specified time interval. Dynamics - the study of force in relation to The SI unit for speed and velocity is meter motion. per second (m/s) Displacement versus Distance Average speed - the total distance traveled A position - refers to the location of an divided by the total time elapsed object with respect to a reference point or Instantaneous speed – the speed at a origin particular moment in time Example: A student walking from his house Average velocity - the displacement to the school shown in figure 3.1 divided by the total time elapsed He walked to the school 100 m away from his house in 80s. The change in the student’s position is called displacement. Displacement - refers to the straight-line distance between an object’s initial and final positions, with direction toward the final position. Instantaneous velocity – the velocity at a specific instant of time Distance - refers to the total length of path taken by an object in moving from its initial to final position