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PHYSICS 9 REVIEWER PAGE 1 1st Quarter 9 PHYSICS Retalo MULTIPLICATION/DIVISION PH...

PHYSICS 9 REVIEWER PAGE 1 1st Quarter 9 PHYSICS Retalo MULTIPLICATION/DIVISION PHYSICS For multiplication and division, the answer should is the science of the world, really the whole have the same number of significant figures as universe works the term with the fewest number of significant figures. QUANTITIES v.s UNITS SCIENTIFIC NOTATION QUANTITIES - things that are measurable (time, length, current, etc.) For whole number: UNITS - things that are measured in: (second. 8 hours, feet, meters, amperes) 3.00 x 10 Standard form: 300000000 LENGTH MASS TIME AREA For decimal number: -8 1km = 1000m 1kg = 1000g 1hr = 60mins 1km = 0.62mi 3.00 x 10 1m = 100cm 1g = 100cg 1day = 24hrs 1m = 1.09yd Standard form: 0.0000000300 1cm = 10mm 1cg = 10 mg 1min = 60sec 1ft = 0.333yd 1m = 39.37in SCIENTIFIC NOTATION RULES: The base should be always 10 RULES FOR SIGNIFICANT FIGURES The exponent must be a non-zero integer, that means it can be either positive or negative 1. All non-zero numbers ARE significant The absolute value of the coefficient is greater 2. Zeros between two non-zero digits ARE than or equal to 1 but it should be less than 10 significant Coefficients can be positive or negative 3.Leading zeros are NOT significant numbers including whole and decimal numbers 4.Trailing zeros to the right of the decimal ARE The mantissa carries the rest of the significant digits of the number significant 5.Trailing zeros in a whole number with the decimal shown ARE significant FACTORS WHY ERRORS OCCUR 6.Trailing zeros in a whole number with no decimal shown are NOT significant. 1. The measuring device used: 7.Exact numbers have an INFINITE number of Worn-out instruments, like stretched significant figures. measuring tape, can cause inaccurate 8.For a number in scientific notation: N × 10x all measurements, as they may result in longer digits comprising N ARE significant by the first 6 measurements than intended. rules; "10" and "×" are NOT significant. Rusty spring balances can provide incorrect readings, affecting measurement RULES FOR SIGNIFICANT FIGURES results. Improperly calibrated tools, such as a ADDITION/SUBTRACTION weighing scale that doesn't read zero For addition and subtraction, the answer should correctly, have the same number of decimal places as the can lead to inaccuracies in measurements. term with the fewest decimal places. PHYSICS 9 REVIEWER PAGE 1  PHYSICS 9 REVIEWER PAGE 2 1st Quarter 9 PHYSICS Retalo 2. Methods in Getting the Measurement: EXAMPLES OF SYSTEMATIC ERROR Achieving aPcHcuYrSatIeC aSnd precise a. Instrument Calibration If a measuring instrument is consistently measurements requires skill and the use of miscalibrated, such as always reading 0.1 proper measurement techniques. A person grams too high, every measurement taken with who employs appropriate methods is more that instrument will have a systematic error. likely to obtain accurate and precise This error is consistent because it occurs in the results compared to someone who does same direction each time. not. b. Environmental Conditions: 3. Conditions Under Which the Measurement Is Made: Systematic errors can be introduced by The physical condition of the person taking variations in environmental conditions that the measurement can impact the affect the measurement. For example, if you outcome. Trembling or shaky hands due to are measuring the length of a metal rod using sickness or other factors may lead to a ruler and the rod's length changes with difficulties in determining the correct temperature due to thermal expansion or dimensions of the quantity being contraction, this introduces a systematic error. measured. c. Flawed Experimental Design: Environmental factors such as Systematic errors can also result from flaws in temperature, pressure, and lighting can the experimental design. For instance, if you also affect measurement results. For are conducting an experiment to measure the instance, extreme temperature variations acceleration due to gravity by dropping can cause materials to expand or objects from a certain height, but the height is contract, impacting measurements. consistently measured incorrectly due to a design flaw in the apparatus, this will introduce TYPES OF ERROR a systematic error. d. Human Bias: 1. Random Error or unsystematic error. Sometimes, systematic errors can be Random error has no pattern, it is introduced by the person conducting the inconsistent. For example, in your first measurement. If a person consistently reading, you thought it might be too small, overestimates or underestimates values due to then the next reading might be too large. a bias, this introduces a systematic error. For So nobody can predict random error and example, a person might always read a this cannot be avoided, even scientist thermometer a degree higher than the actual doing their experiments. temperature. 2. Systematic Error. e. Instrumental Limitations: Systematic error is a consistent and The design and limitations of the measuring repeatable error due to the kind of device can also lead to systematic errors. For measuring device used as mentioned example, if a ruler has a manufacturing defect above. It is also due to flawed that makes it consistently shorter than it should experimental design. be, all measurements made with that ruler will have a systematic error. PHYSICS 9 REVIEWER PAGE 2  PHYSICS 9 REVIEWER PAGE 3 1st Quarter 9 PHYSICS Retalo TRIGONOMETRIC FUNCTION ACCURACY AND PRECISION Right Triangle: A right triangle is a triangle ACCURACY that has one angle equal to 90 degrees (a To minimize errors in measurement, more trials right angle). This angle is typically denoted by must be made. The mean or average value of the symbol "θ" (theta). these trials will be taken to represent the entire Hypotenuse: The hypotenuse is the side of a set of data. From this,the degree of accuracy right triangle that is opposite the right angle. and precision can be determined. It is the longest side and is always opposite to Accuracy is the closeness or nearness of the 90-degree angle. In a right triangle with measurement to the accepted value. In the sides "a" and "b" and hypotenuse "c," imaginary dart game, the bullseye is the according to the Pythagorean theorem: accepted value. The closer your measurement to thNeG aTHcceptedM vAaSluSe, the more accurate is your LE c2= a2+ b2 measurement. Opposite Side: The side that is opposite to a given angle "θ" (not necessarily the right triangle) is called the opposite side. It is the side that is not one of the two sides that form the angle "θ.“ Adjacent Side: The side that is adjacent to a given angle "θ" (not necessarily the right PRECISION angle) is called the adjacent side. It is one of the two sides that form the angle "θ" and is It is the agreement of several measurements not the hypotenuse. made in the same way. The Formula below will help you determine the precision of one’s measurement TRIGONOMETRY PHYSICS 9 REVIEWER PAGE 3  PHYSICS 9 REVIEWER PAGE 4 1st Quarter 9 PHYSICS Retalo VECTOR FORMULAS FOR TRIGONOMETRY: A quantity that deals inherently with both Finding the parts for right triangle and its magnitude and direction is called a vector degree: quantity. Because direction is an important characteristic of vectors, arrows are used to SOH-CAH-TOA represent them; the direction of the arrow gives the direction of the vector. METHODS OF ADDING VECTORS: opposite sine = hypotenuse adjacent cosine = hypotenuse opposite tangent = adjacent Tip: Using your scientific calculator, When finding the degree of a right triangle click shift + (sin/cos/tan) it will display this symbol (sin -/1 cos -/1 tan- 1) then input the variables. SCALAR AND VECTOR SCALAR A scalar quantity is one that can be described with a single number (including any units) giving its size or magnitude. Some other common scalars are temperature (e.g., 20 C) and mass (e.g., 85 kg). PHYSICS 9 REVIEWER PAGE 4  PHYSICS 9 REVIEWER PAGE 5 1st Quarter 9 PHYSICS Retalo DETERMINING THE VALUES OF COMPONENT VECTORS: example: KINEMATICS IN 1D MOTION refers to the change in position of an object with respect to its surroundings in a given period of time. KINEMATICS deals with the concepts that are needed to describe motion, without any reference to forces. DYNAMICS deals with the effect that forces have on motion. Together, kinematics and dynamics form the branch of physics known as mechanics. DISPLACEMENT is a vector that points from an object’s initial position to its final position and has a magnitude that equals the shortest distance between the two positions. SI Unit of Displacement: meter (m) PHYSICS 9 REVIEWER PAGE 5  PHYSICS 9 REVIEWER PAGE 6 1st Quarter 9 PHYSICS Retalo SPEED AND VELOCITY Average Speed SI Unit of Displacement: meter per second (m/s) *Scalar Quantity example: How far does a jogger run in 1.5 hours (5400 s) if his average speed is 2.22 m/s? Solution: Distance = (Average speed)(Elapsed time) Distance = (2.22 m/s)(5400 s) Distance = 12 000 m In these answers, the algebraic signs convey the directions of the velocity vectors. In particular, for Average Velocity run 2 the minus sign indicates that the average velocity, like the displacement, points to the left in Figure 2.3b. The magnitudes of the velocities are339.5 and 342.7 m/s. ACCELERATION SI Unit of Velocity: meter per second (m/s) Average Acceleration *Vector Quantity example: Andy Green in the car ThrustSSC set a world record of 341.1 m/s (763 mi/h) in 1997. The car was powered by two jet engines, and it was the SI Unit of Acceleration: meter per second (m/s first one officially to exceed the speed of 2) *Vector Quantity sound. To establish such a record, the driver example: makes two runs through the course, one in each Suppose the plane starts from rest when to = 0s. direction, to nullify wind effects. Figure 2.3a The plane accelerates down the runway and at shows that the car first travels from left to right t = 29 s attains a velocity of +260 km/h, where and covers a distance of 1609 m (1 mile) in a the plus sign indicates that the velocity points to time of 4.740 s. Figure 2.3b shows that in the the right. Determine the average acceleration reverse direction, the car covers the same of the plane. distance in 4.695 s. From these data, determine the average velocity for each run. PHYSICS 9 REVIEWER PAGE 6