Mathematical Concepts and Vectors

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Pencasts
Applets and Animations


Student Learning Objectives

Lessons / Lecture Notes

The Physics Classroom (conceptual)

PY105 Notes from Boston University (algebra-based):

Introductory physics notes from University of Winnipeg (algebra-based):

HyperPhysics (calculus-based)

PHY2048 notes from Florida Atlantic University (calculus-based):

PHY2043 notes from Florida Atlantic University (calculus-based)

General Physics I notes from ETSU (calculus-based)


Important Equations

word
pdf



Example Problems

Problem 1  
(a) What is the conversion factor for changing m/s to mi/h? What is the easiest conversion factor to use for a quick approximation?

(b) The density of a neutron star is approximately 1.0 × 1017 kg/m3. Express this density in pounds per cubic inch (lb/in3). (Solutions)

Problem 2
Find the sum of the three displacement vectors in the figure below by using the component method. The magnitude of the vectors are A = 10.0 m, B = 17.0 m, and C = 9.0 m. (Solutions)




Pencasts

Mathematical Concepts and Vectors
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(Note: Please allow ~30 seconds after hitting play for the entire file to load. Click here to download a pdf file of this problem.)


Applets and Animations

Powers of Ten

View the Milky Way at 10 million light years from the Earth. Then move through space towards the Earth in successive orders of magnitude. After that, begin to move from the actual size of a leaf into a microscopic world that reveals leaf cell walls, the cell nucleus, chromatin, DNA and finally, into the subatomic universe of electrons and protons.

Estimation Explore size estimation in one, two and three dimensions! Multiple levels of difficulty allow for progressive skill improvement.
Addition of Vectors
This applet deals with forces exerted on a body (assumed as point-sized). You can vary the number of single forces by using the choice box at the ride side. It is possible to change the sizes and directions of these forces (blue arrows) by dragging the arrowheads to the intended positions with pressed mouse button.
Vector Addition
Learn how to add vectors. Drag vectors onto a graph, change their length and angle, and sum them together. The magnitude, angle, and components of each vector can be displayed in several formats.
Adding Two Vectors A simple demonstration of adding 2 vectors graphically. Also demonstrates that vector addition is commutative.
Adding Three Vectors A simple demonstration of adding 3 vectors graphically. Also demonstrates that vector addition is associative.
Subtracting Two Vectors A simple demonstration that subtracting 2 vectors graphically is the same as adding the first one to the negative of the second one.
Adding Vectors with Components A simple demonstration that to add 2 vectors numerically, just add the cartesian components.
Unit Vectors A simple animation of unit vectors and vector addition.
Dot Product A simple demonstration of the relation between the dot product of 2 vectors and the angle between them.
Cross Product The direction of the cross product of 2 vectors is demonstrated. The magnitude shown is correct but not discussed.