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Payap University General Science Lecture

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- 1. Physics: study of the physical world Apple falls under gravity: a simple physics problem
- 2. Physics: study of the physical world Rock climbing: a physics problem gravity friction energy Force
- 3. Physics: study of the physical world Predicting Global Warming: A complicated physics problem
- 4. Physics: study of the physical world Nano-technology: physicists do it
- 5. Physics: study of the physical world Origin of the universe: a physics problem
- 6. Main Branches of Physics Mechanics Electromagnetics Thermodynamics Quantum Mechanics Relativity Nuclear Physics Grand Unified Theory? Rigid body mechanics Fluid mechanics Light & optics Electrical engineering Atomic & molecular physics Nanotechnology Astrophysics Statistical mechanics
- 7. Problem Solving <ul><li>Outline of a useful problem-solving strategy </li></ul><ul><li>can be used for most types of physics problems </li></ul><ul><li>Can also be used for many types of problems in life </li></ul>Important!
- 8. Math Basics Scalars & Vectors Dimensions & Units Geometry & Trigonometry f(x) A ϑ
- 9. Scalars and Vectors <ul><li>Scalar: magnitude only </li></ul><ul><ul><li>e.g.: 30 cookies </li></ul></ul><ul><li>Vector: magnitude and direction </li></ul><ul><ul><li>e.g.: 45 Newtons of force, upwards </li></ul></ul>In physics, various quantities are either scalars or vectors.
- 10. Distance: Scalar Quantity Distance is the path length traveled from one location to another. It will vary depending on the path. Distance is a scalar quantity – it is described only by a magnitude.
- 11. Speed: Scalar Quantity Speed is distance ÷ time Since distance is a scalar, speed is also a scalar (and so is time) Instantaneous speed is the speed measured over a very short time span. This is what a speedometer in a car reads. Average speed is distance ÷ some larger time interval
- 12. Distance and Speed: Scalar Quantities Average speed is the distance traveled divided by the elapsed time: <ul><li>A bar over something usually denotes the average, also sometimes used: < S > </li></ul><ul><li>A Δ (Greek: delta) is usually used to indicate a difference or interval (Δt = t 2 -t 1 ) </li></ul>
- 13. Displacement: a Vector Displacement is a vector that points from the initial position to the final position of an object.
- 14. Vectors & dimensions <ul><li>A vector has both magnitude and direction </li></ul><ul><li>In one dimension, a vector has one component. </li></ul><ul><li>In two dimensions, a vector has two components. </li></ul><ul><li>In three dimensions, vectors have three components… </li></ul>A vector is usually drawn as an arrow. It is often symbolized with a small arrow over (or sometimes under) a symbol: A
- 15. Addition of vectors Graphical addition
- 16. Vector Quantities: Velocity Note that an object ’s position coordinate may be negative, while its velocity may be positive – the two are independent. Velocity is a vector that points in the direction that an object is moving in
- 17. 2-D Geometry review Curves of functions: y = f(x) f(x) x Slope of curve Δy / Δx
- 18. 2-D Geometry review Linear functions: slope is always the same, constant General functions: slope depends on position
- 19. Vector Quantities Different ways of visualizing uniform velocity :
- 20. Vector Quantities This object ’s velocity is not uniform. Does it ever change direction, or is it just slowing down and speeding up? Visualizing non-uniform velocity :
- 21. More 2-D Geometry Pythagorean Theorem: a 2 + b 2 = h 2
- 22. More 2-D Geometry Angles are in units of degrees or radians (on calculator, be sure to know which is used!) How to convert? Ψ Angles
- 23. More 2-D Geometry Ψ Trigonometry:
- 24. More 2-D Geometry Sin and Cos are always < 1
- 25. More 2-D Geometry Properties of sine and cosine <ul><li>Use: </li></ul><ul><li>All periodic things </li></ul><ul><li>Angles and directions </li></ul>
- 26. One last mathematical tidbit Quadratic Formula: memorize it If faced with an equation where the unknown variable is squared, re-arrange things to look like this: Then x is given by: (There are two possible solutions)
- 27. Vectors in 2-D Vectors have components The magnitude of a vector and the direction of a vector are related to the components Use trigonometry and Pythagoras A x = A cos( ) A y = A sin( )
- 28. Manipulating Vectors in 2-D Adding things in one dimension is easy: 3 Apples + 2 Apples = 5 Apples But in two (or more) dimensions: we add the components: if we have a vector {x Apples, y Oranges} {2 Apples, 3 Oranges} + {5 Apples, 2 Oranges} = (2+5) Apples, (3+2) Oranges = 7 Apples, 5 Oranges
- 29. Vector Components Review If you know A and B, here is how to find C:
- 30. Vector components Review The components of C are given by: And
- 31. Vector Addition and Subtraction Vectors are resolved into components and the components added separately; then recombined to find the resultant vector.
- 32. Example Addition of vectors: adding components So what’s length of R, and direction of R?
- 33. Example Addition of vectors: adding components

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