## Summary

Most things we encounter in Physics are either

scalarsorvectors.## A scalar quantity has only magnitude and no direction.

This means we can fully explain a

scalarwith a number and a unit.## A

vectorquantity has both magnitude and direction.The distinction between scalars and vectors is important. We will use bold face type to indicate a vector, such as

r. In writing a vector by hand, we will indicate a quantity is a vector by drawing an arrow above it as . Some such distinguising notation isimportant.Do not write a vector without some distinguishing characteristic or notation.Consider adding two vectors together as in

A+B=C. Each vector can first beresolvedinto its respective components,A= (A_{x}, A_{y}, A_{z})

B= (B_{x}, B_{y}, B_{z})The components are then added as the scalars they are and the new vector sum is reconstructed,

C= (C_{x}, C_{y}, C_{z})where

C_{x}= A_{x}+ B_{x}C

_{y}= A_{y}+ B_{y}and

C_{z}= A_{z}+ B_{z}We will often write this using

unit vector notationasA= A_{x}i+ A_{y}j+ A_{z}k

B= B_{x}i+ B_{y}j+ B_{z}k

C= C_{x}i+ C_{y}j+ C_{z}kwhere

C_{x}= A_{x}+ B_{x}C

_{y}= A_{y}+ B_{y}and

C_{z}= A_{z}+ B_{z}or

C=A+B

C= (A_{x}+ B_{x})i+ (A_{y}+ B_{y})j+ (A_{z}+ B_{z})k

Two dimensional motion with constant acceleration can be handled with vectors. The resulting motion is calledprojectile motionand the path of an object undergoing such motion is aparabola.

Projectile motion-- motion only under the influence of gravity -- is a combination ofhorizontal motion with constant velocity andvertical motion with constant acceleration.

Uniform Circular Motion(UCM) is another example of non-linear motion. UCM requires an accelerationdirected toward the centerof the circle. This acceleration is called thecentripetalacceleration ("centripetal" means center-seeking). This centripetal acceleration isa _{c}= v^{2}/r

Return to ToC, Vectors and 2D Motion(c) 2002, Doug Davis; all rights reserved