1. PHYS 151 Dr. Richard A Lindgren University of Virginia USA

2. Course Lecture Notes http://people.virginia.edu/~ral5q/PHYS_151_Hue
Textbook: Physics for Scientist and Engineers Fourth Edition
Author Giancoli

3. Physics for Scientists & Engineers, with Modern Physics, 4th edition
Lecture PowerPoints
Chapter 1
Physics for Scientists & Engineers, with Modern Physics, 4th edition
Giancoli

4. Final Grade Determination
Attendance
Homework
Quiz 1 March 11 Friday
Quiz 2 March 25 Friday
Final March 31 Thursday

5. Syllabus Second Week Monday Mar 7 Ch. 4 Newton’s Laws of Motion
Tuesday Mar 8 Ch 4
Wednesday Mar 9 Ch 5 Fricton, Drag forces, and Circular motion
Thursday Mar 10 Ch 5 Fricton, Drag forces, and Circular motion
Friday Mar 11
Ch 6 Gravitation
First Week
Tuesday Mar 1 Ch. 1 Measurement and Estimating
Wednesday Mar 2 Ch. 2
Projectile Motion
Thursday Mar 3
Ch 2 Questions
Ch. 3 Kinematics in 2D
Friday Mar 4 Ch. 3
Kinematics in 2D

6. Syllabus Fourth Week Third Week Monday Mar 21 Monday Mar 14 Quiz 1
Ch. 9 Linear Momentum
Tuesday Mar 22
Quiz 2
Wednesday Mar 23 Ch 10 Rotational Motion
Thursday Mar 24 Ch 10 Rotational Motion
Friday Mar 25 Ch 11 Angular Momentum
Third Week
Monday Mar 14 Quiz 1
Ch 6 Gravitation
Tuesday Mar 15 Ch. 7 Work and Energy
Wednesday Mar 16
Ch. 7 Work and Energy
Ch 8 Conservation of Energy
Thursday Mar 17 Ch 8 Conservation of Energy
Friday Mar 18 Ch. 9
Linear Momentum

7. Syllabus Fifth Week Monday Mar 14 Ch 11 Angular Momentum
Ch 12 Static Equilibrium
Tuesday Mar 15 Ch. 12
Static Equilibrium
Wednesday Mar 16 Review for Final
Thursday Mar 17 Final
Friday

8. Assignment 1 Chp 1 1-33,1-52 Chp 2 2-39, 2-72 Chp 3 3-22, 3-84
Due Monday 10:00 Mar 7

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

10. 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

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

12. 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.

13. 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.

14. 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

15. 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.
Force=ma [F]=[M][L]/[T2]

16. Estimates or Guesstimates– How a Little Reasoning Goes a Long Way
Estimates are very helpful in understanding what the solution to a particular problem might be.
Generally an order of magnitude is enough – is it 10, 100, or 1000?
Final quantity is only as accurate as the least well estimated quantity in it

17. 1) How many golf balls would it take to circle the equator?
2) If we gave every family on earth a house and a yard, what per cent of the earth’s surface would they occupy? 3)How many cells are there in the human body? 4) What is the total amount of human blood in the world?

18. Guesstimates
1) How many golf balls would it take to circle the equator?
You need the diameter of the golf ball which is about 2 inches or 4 cm.
2.5 cm = 1 inch
And you need the circumference of the earth. ????
Divide the circumference by the diameter to get the number of golf balls
How to estimate the circumference of the earth?
US is 3000 miles wide because it takes a jet at 500 mph to fly from NY to LA in 6 hours
It is also 3 times zones wide and there are 24 time zones across the world
and therefore the circumference is 3000 x 24/3=24,000 miles or 40,000 km

19. In this course we will mostly work with three types of forces
Projectile motion – Gravity
Book resting on a table. What forces act on the book?
Friction
Gravity
Contact force
……….
Rigid Bodies
Also keep in mind that we assume in many instances when we have contact interactions, we assume also that we are dealing with rigid bodies. In actual fact a body is never purely rigid.

20. Matter: What do we mean by it? Solids, Liquids and Gases
Electrons orbiting the nucleus make up the atoms and the atoms make up the solids, liquids and gases.
For example the surface of a solid might look something like this.

21. Solids STM images of a surface through silicon
Atoms are arranged in a crystalline array or 3D solid
Note defects in the lower image

22. Ordinary matter on earth is made up of tiny Atoms

23. Other Interactions Four types four types of such interactions also called fundamental interactions.
Strong - inside the nucleus of the atom
Electromagnetic - between charged particles
Electric
Magnetic
Weak - involves the neutrino
Gravitational – Man - Earth
Strength : Strong > electromagnetic >
weak > gravitational

24. 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

25. Math Review Algebra - Trigonometry and geometry Vectors Derivatives
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

26. Arc Length and Radians S
is measured in radians

27. Pythagorean Theorem
EXAMPLE

28. Trigonometry
EXAMPLE

29. Simultaneous Equations
FIND X AND Y

30. Cramer’s Rule

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

32. Example

33. Derivation
Complete the Square

34. 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

35. 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

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

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

38. Adding Two Vectors
Note you add x and
y components .

39. Vector components in terms of sine and cosiney x q r

40. Scalar product =
90 deg θ AB
Also

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

42. Vectors in 3 Dimensions

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

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

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

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

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

48. 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?

49. 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.

50. 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?

51. 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.