Physics: Vectors and Scalars
Cross product: when theta is 90, AxB=
(|A|)(|B|)
Dot product: if A and B are in the same direction, answer is?
(|A|)(|B|)
+/- : QI, cos
+
+/- : QI, sin
+
+/- : QI, tan
+
+/- : QII, sin
+
+/- : QIII, tsn
+
+/- : QIV, cos
+
+/- : QII, cos
-
+/- : QII, tan
-
+/- : QIII, cos
-
+/- : QIII, sin
-
+/- : QIV, sin
-
+/- : QIV, tan
-
What are the three ways a vector can be written? (10 m/s up)
- 10 m/s up - 10 m/s @ 90° (polar) - 10 m/s j hat (Cartesian)
What are three ways a vector can be written? (gravitational acceleration)
- 9.80065 m/s^2 down - -9.80065 m/s^2 @ 270° - 9.80065 m/s^2 j hat
What can you assume of the x- and y-components every single time?
- Ax is less than or equal to A(vector) - Ay is less than or equal to A(vector)
How can you decide if the vectors have the same unit?
- just looking at it (m=m) - dimensional analysis
When do the x-components equal the magnitude of A?
- magnitude = 0 - direction of vector @ 0° - direction of vector @ 180°
Dot product: if A and B are in opposite directions, answer is?
-(|A|)(|B|)
What is tan(-45°)?
-1
Cross product: what is another way to write AxB?
-BxA
Cross product: when theta is 180, AxB=
0
Dot product: if A and B are perpendicular, answer is?
0
What is tan(45°)?
1
How do you convert a negative magnitude to a positive magnitude without changing the value of a vector?
1. drop the negative sign 2. add/subtract 180° to/from the direction
For what specific values does tan not exist?
90°, 270°, 450°, etc -90°, 270°, 450°, etc
How is a x-component signified?
A subscript of x (A's x component is Ax)
How is the y-component signified?
A subscript of y (A's y-component is Ay)
What is the formula to find the x-component?
Ax=|A(vector)|*cos(theta)
What is the formula to find the y-component?
Ay=|A(vector)|*sin(theta)
In the 4 quadrants, where is tan + ?
QI and QIII (where sin and cos are same sign)
In the 4 quadrants, where is tan - ?
QII and QIV (where sin and cos are diff signs)
How is the resultant vector signified?
R (with arrow on top)
What is a vector?
a physical quantity defined by magnitude and direction
What is a scalar?
a physical quantity defined by magnitude only
When you add/subtract vectors, is the result a vector or a scalar?
a vector
What is a unit vector?
a vector with a magnitude of one that points in a specific direction
What are some vectors?
acceleration, velocity, displacement, position, (force, momentum, impulse, torque)
How do you make a negative degree value positive?
add 360° (exact value)
What represents vectors?
arrows
In the 4 quadrants, where is sin - ?
bottom half, QIII and QIV
How do you move in the negative direction for r?
clockwise direction
When given scale and length, how do you find magnitude?
conversion, multiply length by scale
Positive y-axis, +/- : cos, sin, tan
cos = 0 sin: + tan: DNE
Positive x-axis, +/- : cos, sin, tan
cos: + sin = 0 tan = 0
Negative x-axis, +/- : cos, sin, tan
cos: - sin = 0 tan = 0
Negative y-axis, +/- : cos, sin, tan
cos=0 sin: - tan: DNE
How do you move in the positive direction for r?
counterclockwise direction
What are some scalars?
distance, speed, time, mass, temperature, (energy, work, power)
Cross product: AxB = BxA - true or false?
false (same magnitude, opposite directions)
Cross product: how does the right hand rule work?
hand along first one, curl fingers toward second, thumb direction is direction
What is the unit vector along the positive x-axis?
i hat
In what direction should a vector arrow be pointed?
in the direction of the vector
What is the unit vector along the positive y axis?
j hat
What is the unit vector along the positive z axis?
k hat
In the 4 quadrants, where is cos - ?
left, QII and QIII
What does the left side of scale represent?
length on paper
What does the length of a vector arrow represent?
magnitude
What does the right side of the scale represent?
magnitude represented
Do unit vectors have a unit?
no
Does A(vector)-B(vector) equal B(vector)-A(vector)?
no, these are opposite directions
Cross product: when theta is 0, AxB=
o
When multiplying a vector by a scalar, what part of the vector do you use?
only the magnitude (NOT the direction)
Dot product: focuses on what components?
parallel
Cross product: focuses on what components?
perpendicular
What is the x-component?
portion of the vector along the x axis
What is the y-component?
portion of the vector along the y axis
Cross product: how is direction determined?
right hand rule
In the 4 quadrants, where is cos + ?
right, QI and QIV
Dot product: result is a scalar or a vector?
scalar
What should be at the top of vector graphs?
scale
What is the resultant vector?
sum of two or more vectors; distance from origin to the last tip of the vectors
Cross product: under what condition does the formula work?
theta is between A and B
Dot product: Under what condition does the formula work?
theta is between A and B
In the 4 quadrants, where is sin + ?
top half, QI and QII
Cross product: example?
torque
Cross product: results in a vector or scalar?
vector
When multiplying a vector by the scalar, is the result a vector or a scalar?
vector
Under what stipulation does adding vectors function?
vectors must have the same unit
What appears on the graph when tan does not exist?
vertical asymptote
When converting a negative magnitude to a positive magnitude, when do you add 180°?
when direction is less than 180°
When converting a negative magnitude to a positive magnitude, when do you subtract 180°?
when the direction is greater than or equal to 180°
Dot product: an example?
work
Where does tan=0?
x-axis
Where is sin=0?
x-axis
Rx is what?
x-component of resultant vector
Where is cos=0 ?
y-axis
Where does tan not exist? (general)
y-axis, when cos=0
Ry is what?
y-component of the resultant vector
Does A(vector)-B(vector) equal A(vector) + -B(vector)?
yes