Vector Mathematics
Adding, Subtracting, Multiplying and Dividing
Why?
One can add 23 kg and 42 kg and get 65 kg. However, one cannot add together 23 m/s south and 42 m/s southeast and get 65 m/ s south-southeast. Vectors addition takes into account addin
Two Dimensional Motion
AP Physics C
Position and Velocity Vectors
r = xi + yj + zk r vav = t dr v= dt
At every point along a path, the instantaneous velocity vector is tangent to the path at that point
Components of Instantaneous Velocity
dx vx = dt dy
Rotational Motion
AP Physics C
Introduction
The motion of a rigid body (an object with a definite shape that does not change) can be analyzed as the translational motion of its center of mass AND the rotational motion about its center of mass. All points
One Dimensional Motion
AP Physics C
Terms
Displacement vs. Distance Displacement: Change in position (vector) Distance: How far an object has travelled (scalar) Symbol: x or x SI Unit: meter, m
Position
x = x f xi
Terms
Velocity vs. Speed Velocity: Rate
6.1: Antiderivatives
Greg Kelly, Hanford High School, Richland, Washington
First, a little review: Consider: then:
y = x2 + 3
y = 2 x
or
y = x2 5
y = 2 x
It doesnt matter whether the constant was 3 or -5, since when we take the derivative the constant dis
Flux and Gauss' Law
Ch 22 AP Physics C
Background
Gauss Law is part of the key to using symmetry considerations to simplify EField calculations (remember section 21.5 when we integrated to solve for E of a ring of charge, line of charge etc.) In chapter
Flux and Gauss' Law
Ch 22 AP Physics C
Background
Gauss Law is part of the key to using symmetry considerations to simplify EField calculations (remember section 21.5 when we integrated to solve for E of a ring of charge, line of charge etc.) In chapter
Forces
Qu es un Force? A push or a pull
The Four Fundamental Forces in Nature
1. Gravitational 1. Electromagnetic 1. Strong Nuclear 1. Weak Nuclear
Galileo
1564 - 1642 Was a Copernican Convicted of Heresy 1633 Pardoned by Pope in 1992
Galileo
Studied F
Equilibrium
Things not Moving (sweet)
Everyday Forces
1. Weight: This is the force of gravity. Or gravity acting on a mass
w = mg
2. Normal Force: The force a surface applies to an object. It is ALWAYS perpendicular to surface
Everyday forces cont.
1. Ten
Work, Energy, and Power
Work
Work is the product of the magnitude of the displacement and the component of the force acting in the direction of the displacement
W = F s (dot product) W = ( F cos ) s W = Fd cos
Work
Most of the time F is in the directi
Electrostatics
Nay, electrophun!
History
The word electricity comes from the Greek elektron which means amber. The amber effect is what we call static electricity.
History
Ben Franklin made the arbitrary choice of calling one of the demo situations posi
3.1
Photo by Vickie Kelly, 2003
Derivatives
Greg Kelly, Hanford High School, Richland, Washington
Great Sand Dunes National Monument, Colorado
f ( x) y dy dx df dx
f prime x y prime
or
the derivative of f with respect to x
dee why dee ecks
or
the derivati
3.6
The Chain Rule
Greg Kelly, Hanford High School, Richland, Washington
Photo by Vickie Kelly, 2002
U.S.S. Alabama Mobile, Alabama
Photo by Vickie Kelly, 2002
Greg Kelly, Hanford High School, Richland, Washington
We now have a pretty good list of shortcu