AP Physics C: Mechanics
AP Physics C: Mechanics Fundamentals of Physics 7e – Chapter 3 Mrs. Hill
Scalars Quantity without direction Examples:
Temperature Pressure Energy Mass Time
Vectors Quantities with both magnitude and direction Examples:
Displacement Velocity Acceleration
Displacement as a vector
Displacement does not depend on the path taken Can be represented by an arrow (or vector)
Vectors on a graph
Vectors can be placed anywhere on a set of axes Must maintain magnitude (length) and angle Multiple copies of the same vector
Adding Vectors
Two methods: Parallelogram Tip-to-tail
Adding Vectors
Commutative property: A
+B=B+A
Adding Vectors
Associative Property A
+ (B + C) = (A + B) + C
Adding Multiple Vectors
Move vectors around the axes so that they meet tip to tail You can add vectors in any order
Subtracting Vectors
A – B = A + (-B) A negative vector has the same magnitude, just pointing 180o from the original angle
Vector Components
Every 2-D vector can be broken up into its components – axis y – axis x
Add each component for the resultant vector’s components
Practice #1 A commuter airplane starts from an airport and flies to city A located 175 km in a direction 30o north of east. Next, it flies 150 km 20o west of north to city B. Finally, it flies 190 km due west to city C. Find the location of city C relative to the location of the starting point.
**Start with a diagram**
Practice #1
Practice #1 How do we calculate the magnitude of the resultant vector? How do we calculate the angle of the resultant vector?
Trig Identities
SOH CAH TOA sin θ = opposite / hypotenuse cos θ = adjacent / hypotenuse tan θ = opposite / adjacent
Dot Product
a b
a b b a
b a
“a dot b” ab cos ba cos =
a b
(cosine is symmetric)
Dot Product – Unit Vector
a b
ax bx
ay by
Answer is a scalar!
az bz
Cross Product
a b
a b
a b
“a cross b” sine is opposite itself ab sin
b a
Cross Product – Unit Vector a b
ay bz
^
by az i
a z bx
^
b z ax j
ax b y
^
bx a y k
Scalars Quantity without direction Examples:
Temperature Pressure Energy Mass Time
Vectors Quantities with both magnitude and direction Examples:
Displacement Velocity Acceleration
Displacement as a vector
Displacement does not depend on the path taken Can be represented by an arrow (or vector)
Vectors on a graph
Vectors can be placed anywhere on a set of axes Must maintain magnitude (length) and angle Multiple copies of the same vector
Adding Vectors
Two methods: Parallelogram Tip-to-tail
Adding Vectors
Commutative property: A
+B=B+A
Adding Vectors
Associative Property A
+ (B + C) = (A + B) + C
Adding Multiple Vectors
Move vectors around the axes so that they meet tip to tail You can add vectors in any order
Subtracting Vectors
A – B = A + (-B) A negative vector has the same magnitude, just pointing 180o from the original angle
Vector Components
Every 2-D vector can be broken up into its components – axis y – axis x
Add each component for the resultant vector’s components
Practice #1 A commuter airplane starts from an airport and flies to city A located 175 km in a direction 30o north of east. Next, it flies 150 km 20o west of north to city B. Finally, it flies 190 km due west to city C. Find the location of city C relative to the location of the starting point.
**Start with a diagram**
Practice #1
Practice #1 How do we calculate the magnitude of the resultant vector? How do we calculate the angle of the resultant vector?
Trig Identities
SOH CAH TOA sin θ = opposite / hypotenuse cos θ = adjacent / hypotenuse tan θ = opposite / adjacent
Dot Product
a b
a b b a
b a
“a dot b” ab cos ba cos =
a b
(cosine is symmetric)
Dot Product – Unit Vector
a b
ax bx
ay by
Answer is a scalar!
az bz
Cross Product
a b
a b
a b
“a cross b” sine is opposite itself ab sin
b a
Cross Product – Unit Vector a b
ay bz
^
by az i
a z bx
^
b z ax j
ax b y
^
bx a y k
