Payap University General Science Lecture

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

8. Math Basics Scalars & Vectors Dimensions & Units Geometry & Trigonometry f(x) A ϑ

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

13. Displacement: a Vector Displacement is a vector that points from the initial position to the final position of an object.

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

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