Vectors
Bellwork ( Clickers )
Some Notes
Stations ( Take Notes!! )
Open Notes/Book Quiz on Thur ( 09/13/12 )
What’s On Quiz – 6 Qs
• Conceptual Questions on Vectors
– Conceptual Clickers / Stations
• Finding resultants/angles of vectors (free-response)
– Graphical and Analytical
– AP will have 3 of these ( Honors only 2 )
Question 3.2a
Vector Components I
a) it doubles
If each component of a
vector is doubled, what
happens to the angle of
that vector?
b) it increases, but by less than double
c) it does not change
d) it is reduced by half
e) it decreases, but not as much as half
Question 3.2a
Vector Components I
a) it doubles
If each component of a
vector is doubled, what
happens to the angle of
that vector?
b) it increases, but by less than double
c) it does not change
d) it is reduced by half
e) it decreases, but not as much as half
The magnitude of the vector clearly doubles if each of its components is
doubled. But the angle of the vector is given by tan q = 2y/2x, which is the
same as tan q = y/x (the original angle).
Follow-up: if you double one component and not the
other, how would the angle change?
Question 3.2b
Vector Components II
A certain vector has x and y components that are
equal in magnitude. Which of the following is a
possible angle for this vector in a standard x-y
coordinate system?
a) 30°
b) 180°
c) 90°
d) 60°
e) 45°
Question 3.2b
Vector Components II
A certain vector has x and y components that are
equal in magnitude. Which of the following is a
possible angle for this vector in a standard x-y
coordinate system?
a) 30°
b) 180°
c) 90°
d) 60°
e) 45°
The angle of the vector is given by tan q = y/x. Thus, tan q = 1 in this
case if x and y are equal, which means that the angle must be 45°.
The Components of a Vector
**Notice arrow above and bold font / Angle goes counterclockwise!!
Can resolve vector into perpendicular components using a twodimensional coordinate system:
The Components of a Vector
Length, angle, and components can be calculated from each
other using trigonometry:
The Components of a Vector
Signs of vector components:
Adding and Subtracting Vectors
Adding vectors graphically: Place the tail of the second at the
head of the first. The sum points from the tail of the first to the
head of the last.
Finding Vector Resultants
• Graphical method is approximate
– Limited by accuracy of graph, measurements, etc.
• Using components ( analytical ) is more
accurate
Outdoor Lab Example
Light-pole
Building
Resultant ( Sum )
Tree
Components
Adding and Subtracting Vectors
Adding Vectors Using Components:
1. Find the components of each vector to be added.
2. Add the x- and y-components separately.
3. Find the resultant vector.
Adding and Subtracting Vectors
Adding and Subtracting Vectors
Subtracting Vectors: The negative of a vector is a vector of the same magnitude
pointing in the opposite direction. Here,
.
D= A  B
Examples
•
•
•
•
Ax = (5.00 m)*cos 60.0o Ay = (5.00 m)*sin 60.0o
Bx = (4.00 m )*cos 20.0o By = (4.00 m )*sin 20.0o
Add x and y components separately
Cx is 6.26 m
and
Cy is 5.70 m
Adding and Subtracting Vectors
Examples – Take a Step Further
Examples – Take a Step Further
Stations – Take Notes!!
• #1 – Basic conceptual / 1D Kinematics review
– Average speed ( distance / time )
– Average velocity ( displacement / time or:
• #2 – Basic Resolution of Vector into Components
• #3 – Vector Addition ( starts empty )
• #4 – PhET Vector Addition Simulation
• #5 – Playing with Force Table at front of room
Question 3.3
Vector Addition
You are adding vectors of length 20
a) 0
and 40 units. What is the only
b) 18
possible resultant magnitude that
c) 37
you can obtain out of the following
d) 64
choices?
e) 100
Question 3.3
Vector Addition
You are adding vectors of length 20
a) 0
and 40 units. What is the only
b) 18
possible resultant magnitude that
c) 37
you can obtain out of the following
d) 64
choices?
e) 100
The minimum resultant occurs when the vectors are
opposite, giving 20 units. The maximum resultant
occurs when the vectors are aligned, giving 60 units.
Anything in between is also possible for angles
between 0° and 180°.