Summary

Most things we encounter in Physics are either scalars or vectors.

A scalar quantity has only magnitude and no direction.

This means we can fully explain a scalar with a number and a unit.

A vector quantity 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 is important. 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 be resolved into 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 notation as

A = 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 k

where

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

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Two dimensional motion with constant acceleration can be handled with vectors. The resulting motion is called projectile motion and the path of an object undergoing such motion is a parabola.

Projectile motion -- motion only under the influence of gravity -- is a combination of

horizontal motion with constant velocity and

vertical motion with constant acceleration.

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Uniform Circular Motion (UCM) is another example of non-linear motion. UCM requires an acceleration directed toward the center of the circle. This acceleration is called the centripetal acceleration ("centripetal" means center-seeking). This centripetal acceleration is

a_c = v²/r

Unit Vectors			Homework
Return to ToC, Vectors and 2D Motion

(c) 2002, Doug Davis; all rights reserved