Strategies of Studying Physics
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1 Strategies of Studying Physics Chin-Sung Lin
2 Strategies of Studying Physics q Use physics words with precision q Know the concepts behind the formulas q Apply dimensional analysis q Develop problem solving skills q Think through the math
3 Physics Words
4 Use Physics Words with Precision Definition of Physics Words q Physics words have precise definitions q May be different from their regular English meanings q Engage in physics talk Speed Gravity Distance Impulse Displacement Momentum Work Velocity Energy Normal Power Force Field Potential Current Acceleration
5 Physics Concepts
6 Know the Concepts behind the Formulas Context of Physics Formulas q Physics formulas has conditions attached to them F net = ma W = Fd Net force Any force
7 Know the Concepts behind the Formulas Context of Physics Formulas q Concepts and principles form the basis of formulas mgh A + ½ mv A 2 = mgh B + ½ mv B 2 PE A + KE A = PE B + KE B E TA = E TB Conservation of Energy
8 Know the Concepts behind the Formulas Context of Physics Formulas q Engage in the concept explaining process q Any forms of teaching, explaining, or writing physics
9 Know the Concepts behind the Formulas Teaching & Writing Process (Research Results) q Based on a student teaching research:
10 Know the Concepts behind the Formulas Data Comparison - Definition Assume: t i is the teaching score of i th student r i is the Regents score of i th student p i is the predicted Regents score of i th student based on t i where i = 1, 2, 3, 12
11 Know the Concepts behind the Formulas Data Comparison - Objective Function Define an objective function M: the root-mean-square (rms) value of the difference between r i and p i 12 M = Σ (r i - p i ) 2 /12 I = 1
12 Know the Concepts behind the Formulas Regents Scores Prediction (A Linear Function of Teaching Scores) Results p i = f(t i ) = 1.9 t i or p = f(t) = 1.9 t M = 15.4 for all students M = 3.5 excluding 3 exceptions
13 Regents Test Score Prediction I (A Linear Function of Teaching Scores) Regents Test Scores vs. Predictions Score Score Prediction Student
14 Know the Concepts behind the Formulas Data Comparison - Definition Assume: s 1i - ave. test score of 1 st mp for i th student s 2i - ave. test score of 2 nd mp for i th student d i - difference btw s 2i & s 1i for i th student where i = 1, 2, 3, 12 d i = s 2i - s 1i
15 Know the Concepts behind the Formulas Regents Scores Prediction (A Linear Function of Teaching Scores and Test Scores) Results p i = f(t i, d i ) = t i d i or p = f(t, d) = t d M = 13.3 for all students M = 1.9 excluding 3 exceptions
16 Regents Test Score Prediction II (A Linear Function of Teaching Scores and Test Scores) Regents Test Scores vs. Prediction Score Score Prediction Student
17 Know the Concepts behind the Formulas Teaching & Writing Process (Research Results) q Based on a student teaching research: Teaching scores is a strong predictor for the Regents test The trend of the average test score serves as a modifier The impact of teaching scores is five times stronger than the trend of the average test scores Teaching (including writing) represents understanding Teaching (including writing) could strongly improve understanding
18 Dimensional Analysis
19 Apply Dimensional Analysis Derived Units q Know the symbols/definitions of derived units Speed (v): m/s Acceleration (a): m/s 2 Force (F): kg m/s 2 (N, newton) Work (W): kg m 2 /s 2, N m (J, joule) Power (P): kg m 2 /s 3, N m/s (W, watt)
20 Apply Dimensional Analysis Dimensional Analysis q Every equation must be balanced dimensionally q Units on both sides of the equation must be identical d = v t + ½ a t 2 m = (m/s) s + (m/s 2 ) s 2
21 Apply Dimensional Analysis Dimensional Analysis q Example: If v is velocity, m is mass, a is acceleration, and a = Δv/t and F = ma, find the unit of force (F)
22 Apply Dimensional Analysis Dimensional Analysis q Example: If v is velocity, m is mass, a is acceleration, and a = Δv/t and F = ma, find the unit of force (F) F = m a = m Δv / t Unit of F = kg m/s/s = kg m/s 2
23 Apply Dimensional Analysis Dimensional Analysis q Example: If gravitation force (F g ) can be described by the following formula, find the dimension of G F g = G m 1 m 2 / d 2
24 Apply Dimensional Analysis Dimensional Analysis q Example: If gravitation force (F g ) can be described by the following formula, find the dimension of G F g = G m 1 m 2 / d 2 kg m/s 2 = [G] kg kg / m 2 [G] = m 3 / kg s 2
25 Apply Dimensional Analysis Dimensional Analysis q Unit Conversion Use dimensional analysis to do unit conversion q Example: Find how many seconds per day
26 Apply Dimensional Analysis Dimensional Analysis q Unit Conversion Use dimensional analysis to do unit conversion q Example: Find how many seconds per day? sec = 24 hrs x 60 min x 60 sec = sec 1 day 1 day 1 hr 1 min 1 day
27 Apply Dimensional Analysis Dimensional Analysis q Unit Conversion Use dimensional analysis to do unit conversion q Example: Find how many seconds per day? sec = 24 hrs x 60 min x 60 sec = sec 1 day 1 day 1 hr 1 min 1 day
28 Problem Solving
29 Develop Problem Solving Skills Physics Problem Solving q Encompass many physics concepts, principles, formulas, and mathematical disciplines q Problem solving skills: Analyze problems Associating physics concepts/principles/formulas Apply mathematical skills
30 Develop Problem Solving Skills Physics Problem Solving Steps q Make a sketch q Classify the description q Identify and list all the known & the unknown q Associate with physics concepts, definitions, relationships, formulas, and principles q Form & solve mathematical models
31 Develop Problem Solving Skills Example A block is placed on an incline plane with angle θ. The coefficient of friction between the block and the incline plane is µ. The acceleration due to gravity is g. Find the acceleration of the block a in terms of g, µ and θ
32 Develop Problem Solving Skills Example
33 Develop Problem Solving Skills Example
34 Develop Problem Solving Skills Example
35 Thinking through the Math
36 Thinking through the Math Mathematical Models q Math can describe complex physics phenomena and capture the relationship among physics quantities in an elegant and concise way F net = ma W = Fd V = IR p = mv Q = It P = w/t
37 Thinking through the Math Mathematical Models q You have to analyze physics problems and reduce them into mathematical forms. On the other hand, you can apply physics laws in mathematic forms (formulas) to solve physics problems q Math is a powerful tool for understanding those physics phenomena that go against or beyond our common sense
38 Thinking through the Math Reference Table
39 The End
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