1. 1 Tuesday, Sept. 10: 17:20 – 19:10 Wednesday, Sept. 10: 17:20 – 19:10 Thursday, Sept. 10: 17:20 – 19:10 Building 6, Room 125 (For students of Dr. Al Ramadan) Evening Classes (Chap. 1 and 2)

2. 2 Coordinate systems, vectors and scalars Lecture 05 (Chap. 3) General Physics (PHYS101) www.cmt.ua.ac.be/golib/PHYS101

3. 3 Coordinate Systems Coordinate systems are used to describe the position of an object in space Coordinate system (frame) consists of: ✦ a fixed reference point called the origin ✦ specific axes with scales and labels ✦ instructions on how to label a point relative to the origin and the axes 0x 1 2 3 45 (cm)

4. 4 2D Coordinate Systems Cartesian (rectangular) Polar (plane)

5. 5 Cartesian Coordinate Systems x- and y- axes points are labeled (x,y) y (cm) x (cm)

6. 6 Polar Coordinate Systems the origin and the reference line point is distance r from the origin in the direction of angle, from the reference line points are labeled (r, )

7. 7 Coordinate conversions from polar coordinate to Cartesian coordinate from Cartesian coordinate to polar coordinate

8. 8 Trigonometric functions Pythagorean Theorem c 2 =a 2 +b 2

9. 9 Trigonometric functions Example: how high is the building? Known: angle and one side Find: another side height=dist. tan =(tan 39.0 o )(46.0 m)=37.3 m

10. 10 Scalar and Vector Quantities Scalar quantities are completely described by magnitude only (temperature, mass, time, length...) Vector quantities need both magnitude (size) and direction to completely describe them (force, displacement, velocity...) Represented by an arrow, the length of the arrow is proportional to the magnitude of the vector Head of the arrow represents the direction x

11. 11 Vector Notation When handwritten, use an arrow: When printed, will be in bold print: A normal letter is used for its magnitude:

12. 12 Properties of Vectors Two vectors are equal if they have the same magnitude and the same direction Two vectors are negative if they have the same magnitude but are 180 o apart (opposite direction) The resultant vector is the sum of a given set of vectors

13. 13 Properties of Vectors Any vector can be moved parallel to itself without being affected y x Rotation is not allowed!!!

14. 14 Division and multiplication by a Scalar The result of the multiplication and division is a vector The magnitude of the vector is multiplied or divided by the scalar. If the scalar is positive, the direction of the result vector if the same as of the original vector If the scalar is negative, the direction of the result vector if the opposite as of the original vector

15. 15 Division and multiplication by a Scalar

16. 16

17. 17 Examples: Distance or Displacement? Distance may be, but is not necessarily, the magnitude of the displacement. Distance - scalar quantity. Displacement - vector quantity. displacementdistance