Fundamentals of Physics

1. Fundamentals of Physics Chapter 3 Vectors • Vectors & Scalars • Adding Vectors Geometrically • Components of Vectors • Unit Vectors • Adding Vectors by Components • Vectors & the Laws of Physics • Multiplying Vectors Review & Summary Questions Exercises & Problems Physics 2111 Fundamentals of Physics

2. Vectors & Scalars A scalar quantity only has a magnitude. e.g.: temperature, speed, mass, . . . A vector quantity a magnitude and a direction. e.g.: displacement, velocity, acceleration, . . . All 3 represent the same vector. All 3 paths represent the same displacement vector. Physics 2111 Fundamentals of Physics

3. Adding Vectors Geometrically “head – to – tail” Physics 2111 Fundamentals of Physics

4. Adding Vectors Geometrically Add vectors in either order: Associative Law: Commutative Law: Physics 2111 Fundamentals of Physics

5. Vector Subtraction a vector with the same magnitude but the opposite direction. (See Checkpoint 1) Physics 2111 Fundamentals of Physics

6. Components of Vectors Physics 2111 Fundamentals of Physics

7. Vectors with Components of Different Signs Physics 2111 Fundamentals of Physics

8. Unit Vectors A Unit Vector only specifies a direction. Unit vector magnitude = 1 Unit vector has no units. Unit Vectors in the positive directions of the x, y, z axes: “right-handed coordinate system” Physics 2111 Fundamentals of Physics

9. Proper combinations of ax and ay? Physics 2111 Fundamentals of Physics

10. Adding Vectors by Components Physics 2111 Fundamentals of Physics

11. Adding Vector Components Physics 2111 Fundamentals of Physics

12. Vectors and the Laws of Physics The properties of the vector do not depend on the choice of coordinate system. Physics 2111 Fundamentals of Physics

13. Multiplying Vectors • Multiply a vector by a scalar: • The Scalar Product • The Vector Product Physics 2111 Fundamentals of Physics

14. Example Vector a with magnitude 17.0 m is directed +56.00 counterclockwise from the + x axis. What are the components ax and ay?. A second coordinate system is inclined 18.00 with respect to the first. What are the components of ax’ and ay’? Physics 2111 Fundamentals of Physics

15. Example A= 5.0 m B=15.0m C=18.0 m R= ? (A + B + C), q = ? Physics 2111 Fundamentals of Physics