1. general physics I, lec 1 By: T.A.Eleyan 1 Lecture (2)

2. general physics I, lec 1 By: T.A.Eleyan 2 Scalars and Vectors Scalars have magnitude only. Length, time, mass, speed and volume are examples of scalars. Vectors have magnitude and direction. The magnitude of is written | | Position, displacement, velocity, acceleration and force are examples of vector quantities.

3. general physics I, lec 1 By: T.A.Eleyan 3 Properties of Vectors Equality of Two Vectors Two vectors are equal if they have the same magnitude and the same direction Movement of vectors in a diagram Any vector can be moved parallel to itself without being affected

4. general physics I, lec 1 By: T.A.Eleyan 4 Negative Vectors Two vectors are negative if they have the same magnitude but are 180° apart (opposite directions) Multiplication or division of a vector by a scalar results in a vector for which (a) only the magnitude changes if the scalar is positive (b) the magnitude changes and the direction is reversed if the scalar is negative.

5. general physics I, lec 1 By: T.A.Eleyan 5 Adding Vectors When adding vectors, their directions must be taken into account and units must be the same First: Graphical Methods Second: Algebraic Methods

6. general physics I, lec 1 By: T.A.Eleyan 6 Adding Vectors Graphically (Triangle Method) Continue drawing the vectors “tip-to-tail” The resultant is drawn from the origin of A to the end of the last vector Measure the length of R and its angle

7. general physics I, lec 1 By: T.A.Eleyan 7 When you have many vectors, just keep repeating the process until all are included The resultant is still drawn from the origin of the first vector to the end of the last vector

8. general physics I, lec 1 By: T.A.Eleyan 8 Alternative Graphical Method Parallelogram Method When you have only two vectors, you may use the Parallelogram Method All vectors, including the resultant, are drawn from a common origin The remaining sides of the parallelogram are sketched to determine the diagonal, R

9. general physics I, lec 1 By: T.A.Eleyan 9 Vector Subtraction Special case of vector addition If A – B, then use A+(-B) Continue with standard vector addition procedure

10. general physics I, lec 1 By: T.A.Eleyan 10 Components of a Vector These are the projections of the vector along the x- and y-axes

11. general physics I, lec 1 By: T.A.Eleyan 11 The x-component of a vector is the projection along the x-axis The y-component of a vector is the projection along the y-axis Then,

12. general physics I, lec 1 By: T.A.Eleyan 12 Adding Vectors Algebraically (1)Choose a coordinate system and sketch the vectors (2)Find the x- and y-components of all the vector (3)Add all the x-components This gives R x : (4)Add all the y-components This gives Ry

13. general physics I, lec 1 By: T.A.Eleyan 13 (5)find the magnitude of the Resultant Use the inverse tangent function to find the direction of R:

14. general physics I, lec 1 By: T.A.Eleyan 14 Problem: