Transcript AP Physics C PPT Ch3.

Vectors
(Knight: 3.1 to 3.4)
Scalars and Vectors
Temperature = Scalar
Quantity is specified by a single
number giving its magnitude.
Velocity = Vector
Quantity is specified by
three numbers that give
its magnitude and direction
(or its components in three
perpendicular directions).
Properties of Vectors
Two vectors are equal if they have the same magnitude and direction.
Adding Vectors
Subtracting Vectors
Combining Vectors
Using the Tip-to-Tail Rule
Clicker Question 1
Question: Which vector shows the sum of
A1 + A2 + A 3 ?
Multiplication by a Scalar
Coordinate Systems
and Vector Components
Determining the Components of a Vector
1. The absolute value |Ax| of the x-component Ax is the
magnitude of the component vector Ax .
2. The sign of Ax is positive if Ax points in the positive x-direction,
negative if Ax points in the negative x-direction.
3. The y- and z-components, Ay and Az, are determined similarly.
Knight’s Terminology:
• The “x-component” Ax is a scalar.
• The “component vector” Ax is a
vector that always points along the
x axis.
• The “vector” is A , and it can
point in any direction.
Determining Components
Cartesian and Polar
Coordinate Representations
Unit Vectors
iˆ  (1, 0, 0)  unit vector in +x-direction = "i-hat"
ˆj  (0,1, 0)  unit vector in +x-direction = "j-hat"
kˆ  (0, 0,1)  unit vector in +z-direction = "k-hat"
A  Ax  Ay  Ak  Axiˆ  Ay ˆj  Az kˆ  ( Ax , Ay , Az )
Example:
B  4iˆ  2 ˆj  5kˆ  (4, 2,5)
Working with Vectors
A = 100 ^i m
B = (200 Cos 450 ^i + 200 Cos 450 ^
j)m
= (141 ^
i + 141 ^j ) m
C=A+B
= (100 i m) + (-141 ^i + 141 j^ ) m
= (-41 ^i + 141 ^
j)m
C = [Cx2 + Cy2]½ = [(-41 m)2 + (141 m)2]½ = 147 m
q = Tan-1[Cy/|Cx|] = Tan-1[141/41] = 740
Note: Tan-1  ATan = arc-tangent = the angle whose tangent is …
Tilted Axes
Cx = C Cos q
Cy = C Sin q
Arbitrary Directions
Perpendicular to a Surface
Chapter 3 Summary (1)
Chapter 3 Summary (2)