2009 Physics 2111 Fundamentals of Physics Chapter 3 1 Fundamentals of Physics Chapter 3 Vectors 1.Vectors & Scalars 2.Adding Vectors Geometrically 3.Components of Vectors 4.Unit Vectors 5.Adding Vectors by Components 6.Vectors & the Laws of Physics 7.Multiplying Vectors Review & Summary Questions Exercises & Problems

2009 Physics 2111 Fundamentals of Physics Chapter 3 2 Vectors & Scalars A vector quantity a magnitude and a direction. e.g.: displacement, velocity, acceleration,... All 3 paths represent the same displacement vector. A scalar quantity only has a magnitude. e.g.: temperature, speed, mass,... All 3 represent the same vector.

2009 Physics 2111 Fundamentals of Physics Chapter 3 3 Adding Vectors Geometrically “head – to – tail”

2009 Physics 2111 Fundamentals of Physics Chapter 3 4 Adding Vectors Geometrically Add vectors in either order: Commutative Law: Associative Law:

2009 Physics 2111 Fundamentals of Physics Chapter 3 5 Vector Subtraction (See Checkpoint 1) a vector with the same magnitude but the opposite direction.

2009 Physics 2111 Fundamentals of Physics Chapter 3 6 Components of Vectors

2009 Physics 2111 Fundamentals of Physics Chapter 3 7 Vectors with Components of Different Signs

2009 Physics 2111 Fundamentals of Physics Chapter 3 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”

2009 Physics 2111 Fundamentals of Physics Chapter 3 9 Proper combinations of a x and a y ?

2009 Physics 2111 Fundamentals of Physics Chapter 3 10 Adding Vectors by Components

2009 Physics 2111 Fundamentals of Physics Chapter 3 11 Adding Vector Components

2009 Physics 2111 Fundamentals of Physics Chapter 3 12 Vectors and the Laws of Physics The properties of the vector do not depend on the choice of coordinate system.

2009 Physics 2111 Fundamentals of Physics Chapter 3 13 Multiplying Vectors Multiply a vector by a scalar: The Scalar Product The Vector Product

2009 Physics 2111 Fundamentals of Physics Chapter 3 14 Example Vector a with magnitude 17.0 m is directed counterclockwise from the + x axis. What are the components a x and a y ?. A second coordinate system is inclined with respect to the first. What are the components of a x ’ and a y ’?

2009 Physics 2111 Fundamentals of Physics Chapter 3 15 Example A= 5.0 m B=15.0m C=18.0 m R= ? (A + B + C),  = ?