Vectors

1
Chapter 4

• Vectors

2
Units

• The primary system of units we will use is the
  metric system (meters, kilograms, and seconds).
• Meters (m) units of distance
• Kilograms (kg) units of mass
• Seconds (s) units of time

3
Pythagorean Theorem

• cos ? A/H
• sin ? O/H
• tan ? O/A
• Pythagorean Theorem
• a2 b2 c2
• where a is the adjacent side, b
• is the opposite side, and c is the
• hypotenuse.

4
Types of Quantities

• Scalar a quantity described completely by its
  magnitude
• Written in italicized type (Example A)
• Vector a quantity defined by both its magnitude
  and direction
• Length of vector is equivalent to the magnitude
• Direction of the vector is given by the arrow
• Written in boldface type (Example A)
• Note For two vectors to be equal they must have
  the same magnitude and direction

5
Vector Addition Subtraction

• Collinear Vectors
• Add the magnitudes of vectors pointing in the
  same direction.
• Subtract the magnitudes of vectors pointing in
  opposite directions.
• Perpendicular Vectors use Pythagorean Theorem

5
5
10
3
5
2
?
6
Vectors that are neither collinear or
perpendicular (Component Method)

• Find the x and y components of each vector
• ensuring to use proper sign convention with
• respect to the x-axis.

7
Component Method (cont.)

• Add the x components of each vector to
• determine the resultant vector in the
• x direction.
• Rx Ax Bx Cx
• Add the y components of each vector to
• determine the resultant vector in the
• y direction.
• Ry Ay By Cy

8
Component Method (cont.)

• Use Pythagorean Theorem to determine the
  resultant vector.
• Use the inverse tangent function (tan-1) to
  determine the angle