Chapter 3 Vectors Reading Assignment Chapter 4 1
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Chapter 3: Vectors Reading Assignment: Chapter 4. 1 -4. 3 Homework 3 (due Wednesday, Sept. 7, 2005): Chapter 4: Q 9, 4, 7, 11, 12, 22 • Web. Assign ok? • Everything all right in lab? • Questions? • In this chapter we will learn about vectors, (properties, addition, components of vectors) • Multiplication will come later
Multiplying a vector by a scalar The product m. A is a vector that has the same _____ as A and magnitude m. A. The product –m. A is a vector that has the ______ direction of A and magnitude m. A. Examples: 5 A; -1/3 A
Components of a vector The x- and y-components of a vector: The angle q between vector and x-axis:
The signs of the components Ax and Ay depend on the _______ and they can be positive or negative. (Examples)
Unit vectors • • A unit vector is a _____ vector having a magnitude 1. Unit vectors are used to indicate a ________. i, j, k represent unit vectors along the x-, y- and z- direction i, j, k form a ____________ coordinate system
The __________ for the vector A is: A = A xi + A yj
Vector addition using unit vectors: We want to calculate: R=A+B From diagram: R = (Axi + Ayj) + (Bxi + Byj) R = (Ax + Bx)i + (Ay + By)j The components of R: Rx = Ax + B x Ry = Ay + B y
Vector addition using unit vectors: The magnitude of a R: The angle q between vector R and x-axis:
Blackboard example 3. 2 Once again, dad doesn’t know where he is going. He drives the car - east for a distance of 50 km, - then north for 30 km - and then in a direction 30° east of north for 25 km. (a) Sketch the vector diagram for this trip. (b) Determine the components of the car’s resultant displacement R for the trip. Find an expression for R in terms of unit vectors. (c) Determine magnitude and direction (angle) of the car’s total displacement R.
Polar Coordinates A point in a plane: Instead of x and y coordinates a point in a plane can be represented by its polar coordinates r and q.
Blackboard example 3. 3 The Cartesian coordinates of a point in the x-y plane are (x, y) = (-3. 50, -2. 50). Find the polar coordinates of this point.
