The Work-Energy Theorem
Derivation of the Work-Energy Theorem
It would be easy to simply state the theorem mathematically. However, an examination of how the
theorem was generated gives us a greater understanding of the concepts underlying the equation.
B
The Component Method for Vector Addition and Scalar
Multiplication.
Each entry in the 2-dimensional ordered pair (a, b) or 3-dimensional triplet (a, b, c)is called a
component of the vector. Unless otherwise specified, it is normally understood that the e
The Cross Product
In this section, we will introduce a vector product, a multiplication rule that takes two vectors and
produces a new vector. We will find that this new operation, the cross product, is only valid for our 3dimensional vectors, and cannot
Graphical Addition
Consider the vectors u = (3, 4) and v = (4, 1) in the plane. We know that the sum of these two
vectors is u + v = (7, 5) . Graphically, we see that this is the same as the result we would get by
"picking up" one of the vectors (without
Terms - Vectors
Direction - The direction in which a 2D-vector points can be characterized by a single angle; for
3D-vectors two angles are needed.
Euclidean Space - The name given to all finite-dimensional spaces obtained by taking Cartesian
products of
The Concept of Force and Newton's First Law
Definition of a Force
Since force is the fundamental concept of Dynamics, we must give a clear definition of this concept
before we proceed with Newton's Laws. A force is defined (very practically) as a push or
Introduction to Vectors
In order to represent physical quantities such as position and momentum in more than one
dimension, we must introduce new mathematical objects called vectors. Technically speaking, a
vector is defined as an element of a vector spac
Dot Product
Technically speaking, the dot product is a kind of scalar product. This means that it is an operation
that takes two vectors, "multiplies" them together, and produces a scalar. We don't, however, want
the dot product of two vectors to produce
Newton's Third Law and Units of Force
Newton's Third Law
All forces result from the interaction of two bodies. One body exerts a force on another. Yet we
haven't discussed what force, if any, is felt by the body giving the original force. Experience tells
The Concept of Mass and Newton's Second Law
Now we have both a definition of force, and a vague idea of how forces relate to motion. What we
need is a precise way of relating the two. But even before we do this, we need to define another
concept that play