PHYS Dr. Richard A Lindgren University of Virginia USA

Preliminaries Photograph Class Send me list of Emails Textbook Grades Syllabus Deadlines Assignment 1

Lecture PowerPoints Chapter 1 Physics for Physics for Scientist and Engineers Fourth Edition GiancoliEngineers, with Modern Physics, 4th dition

Final Grade Determination Attendance/Clickers 10% Homework 25% Quizzes 30 % Final 35%

Week 1 Day Date chapter subject 9.00 9.30 10.00 10.30 Mon Jun 5 1&2 Units &1D motion SI system References frames Displacement Average Velocity Tue 6 3 2D motion Vectors & Scalars Projectile Motion Solving Problems Relative Velocity Wed 7 4 Newton's Laws Force First Law Second Law Third Law Thu 8 Weight, Gravity, Normal Force Free-Body Diagrams Problem Solving Problem solving Fri 9 Using Newton's Laws Friction Uniform Circular Motion Dynamics of C.M. Drag/Terminal Velocity

Week 2 Day Date Chap. Main Subject 9.00 9.30 10.00 10.30 Mon Jun 12 6 Assignment 1 Due Gravitation Universal Gravitation Gravity Near the earth's surface Satellites & Weightlessness Kepler's Laws Tue 13 7 Quiz Ch. 1-5 Work Quiz Ch. 1-5 Work Done by a Constant Force Scalar Product Wed Jun 14 7/8 Work & Conservation of Energy Varying Force Work-Energy Principle Conservative Forces Potential Energy Thu 15 8 Conservation of Energy Mechanical Energy Problem Solving Dissipative Forces Fri 16 8/9 Gravitational Potential Energy Potential Energy Diagrams Momentum Conservation of Momentum

Week 3 Day Date Chap. Main Subject 9.00 9.30 10.00 10.30 Mon Jun 19 9 Assignment 2 Due Quiz Ch. 6-9 Collisions & Impulse Conservation Energy & Momentum Elastic Collisions Inelastic Collisions Tue 20 Momentum Quiz 2 Ch. 6-9 Collisions in Two Dimensions Center of Mass Wed 21 10 Rotational Motion Angular Quantities & Vector nature Constant acceleration Torque & Rotational Inertia Solving Problems Thu 22 Rotational Dynamics Determining Inertia Rotational Kinetic Energy Translaton Plus Rotation Rolling Motion & Slowing down Fri 23 11 Angular Momentum Angular Momentum Examples Vector Product & Torque Angular Momentum of a Particle Rotational Analog of 2nd Law

Week 4 Day Date Chap. Subject 9.00 9.30 10.00 10.30 Mon Jun 26 11 Assignment 3 Due Rotations Conserv. of L Kepler's 2nd Law Spinning Top Gyroscope Rotating Frames/Inertial Forces Pseudo, & Coriolis Forces Tue 27 12 Static Equilibrium Conditions for Equilibrium Cantilever, Seesaw, Ladder Stability Balance Stable Equilibrium Hook's Law Stress and Strain, Young's Mdulus Wed Jun 28 Elasticity and Fracture Fracture/Compression/Tension Trusses/Bridges/Domes About Final Exam Thu 29 Make up Assignment 4 due    Fri Jun 30 Final Exam

Deadlines Assignment 1 12-Jun Quiz 1 13-Jun Assignment 2 19-Jun Final Exam 30-Jun

Assignment 1 Due Monday June 12 9:00 AM Check textbook Chapter 1: 17, 24, 47 Chapter 2: 7, 41, 51, 67, 89 Chapter 3: 7, 22, 33, 46, 67, 77, 81 Chapter 4: 7, 18, 24, 32, 33, 48, 73, 78 Chapter 5: 17, 18, 23, 36, 43, 44, 48, 86, 89,100, 84 Red are graded Black are not graded

Read Chapter 1 Tooling up Units, and unit conversions Accuracy and significant figures Dimensional analysis Principles – predict the future Scalars and vectors Math Review One Dimensional Motion

The system of units we will use is the System International (SI) ; the units of the fundamental quantities are: Length – meter Mass – kilogram Time – second

Fundamental Physical Quantities and Their Units Unit prefixes for powers of 10, used in the SI system:

Accuracy and Significant Figures The number of significant figures represents the accuracy with which a number is known. Terminal zeroes after a decimal point are significant figures: 2.00 has 3 significant figures 2 has 1 significant figure.

Accuracy and Significant Figures If numbers are written in scientific notation, it is clear how many significant figures there are: 6. × 1024 has one 6.1 × 1024 has two 6.14 × 1024 has three …and so on. Calculators typically show many more digits than are significant. It is important to know which are accurate and which are meaningless.

Scientific Notation Example Scientific notation: use powers of 10 for numbers that are not between 1 and 10 (or, often, between 0.1 and 100): When multiplying numbers together, you add the exponents algebraically. When dividing numbers, you subtract the exponents algebraically. Example

1-4 Dimensional Analysis The dimension of a quantity is the particular combination that characterizes it (the brackets indicate that we are talking about dimensions): [v] = [L]/[T] Note that we are not specifying units here – velocity could be measured in meters per second, miles per hour, inches per year, or whatever. [a] = [L]/[T]2 Force=ma [F]=[M][L]/[T2]

Principles or Laws Mathematics Predict the future Conservation of Energy Conservation of Momentum Newton's Laws Principle of Relativity Laws of physics work the same for an observer in uniform motion as for an observer at rest. Mathematics Predict the future

Math Algebra - Trigonometry and geometry Vectors Derivatives Integrals Solving simultaneous equations Cramers Rule Quadratic equation Trigonometry and geometry sin, cos, and tan, Pythagorean Theorem, straight line, circle, parabola, ellipse Vectors Unit vectors Adding, subtracting, finding components Dot product Cross product Derivatives Integrals http://people.virginia.edu/~ral5q/classes/phys631/summer07/math-practice.html

Arc Length and Radians S is measured in radians

Pythagorean Theorem EXAMPLE

Trigonometry EXAMPLE

Simultaneous Equations FIND X AND Y

Cramer’s Rule

Quadratic Formula EQUATION: SOLVE FOR X: SEE EXAMPLE NEXT PAGE

Example

Derivation Complete the Square

Small Angle Approximation Small-angle approximation is a useful simplification of the laws of trigonometry which is only approximately true for very small angles. FOR EXAMPLE

Vectors and Unit Vectors Representation of a vector : has magnitude and direction i and j unit vectors x and y components angle gives direction and length of vector gives the magnitude Example of vectors Addition and subtraction Scalar or dot product

Vectors Red arrows are the i and j unit vectors. Magnitude = Angle between A and x axis =

Adding Two Vectors Create a Parallelogram with The two vectors You wish you add.

Adding Two Vectors Note you add x and y components .

Vector components in terms of sine and cosine y x q r

Scalar product = 90 deg θ AB Also

AB is the perpendicular projection of A on B. Important later. θ AB Also

Vectors in 3 Dimensions

For a Right Handed 3D-Coordinate Systems j k x z Right handed rule. Also called cross product Magnitude of

Suppose we have two vectors in 3D and we want to add them y i j k r1 r2 2 5 1 x 7 z

Adding vectors Now add all 3 components i j k x y z r r2 r1

Scalar product = The dot product is important in the of discussion of work. Work = Scalar product

Cross Product = See your textbook for more information on vectors and cross and dot products

ConcepTest 3.1b Vectors II 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other Given that A + B = C, and that lAl 2 + lBl 2 = lCl 2, how are vectors A and B oriented with respect to each other?

ConcepTest 3.1b Vectors II 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other Given that A + B = C, and that lAl 2 + lBl 2 = lCl 2, how are vectors A and B oriented with respect to each other? Note that the magnitudes of the vectors satisfy the Pythagorean Theorem. This suggests that they form a right triangle, with vector C as the hypotenuse. Thus, A and B are the legs of the right triangle and are therefore perpendicular.

ConcepTest 3.1c Vectors III 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other Given that A + B = C, and that lAl + lBl = lCl , how are vectors A and B oriented with respect to each other?

ConcepTest 3.1c Vectors III 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other Given that A + B = C, and that lAl + lBl = lCl , how are vectors A and B oriented with respect to each other? The only time vector magnitudes will simply add together is when the direction does not have to be taken into account (i.e., the direction is the same for both vectors). In that case, there is no angle between them to worry about, so vectors A and B must be pointing in the same direction.