# Mathematical Concepts and Vectors

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

Student Learning Objectives

• To express quantities using correct units and to be able to use scientific notation.
• To understand how to convert from one set of units to another.
• To understand and use proper significant figures.
• To understand basic trigonometric and geometric relations.
• To understand the basic properties of vectors.
• To add and subtract vectors both graphically and using components.

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

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)

Applets and Animations