Chapter 3: Two Dimensional...

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Chapter 3: Two Dimensional

Kinematics

3.1. Vectors in Physics


Q: The1-D Equations of Motion from the

last chapter are OK; but how do we

describe motion in the real 3-D world?

A: With 2-D and 3-D vectors.


Scalars and Vectors

• A scalar is a single numerical value (e.g.

mass, distance, speed) and has magnitude.

• A vector has magnitude (i.e. length) and

direction.

In two dimensions, if

you only know that the

library is 0.5 miles

away, you do not know

its position unless you

also know its direction.


Representing Vectors


Components of Vectors

To resolve a vector means to find its components.

Its components are the lengths of the vector along

specified (orthogonal, i.e. perpendicular) directions.

To say the library

is 4.24 blocks to

the northwest is

the same as to

say it is 3 blocks

north and 3

blocks west.


Trigonometry in 5 Minutes


Computing Vector Components


Example 1


Angle is counterclockwise from the X axis


However in word

problems, watch

out if alternative

angles are given.


From Components to Vectors


Example 2


Example 3


Warning


A certain vector has x and y components

that are equal in magnitude. Which of the

following is a possible angle for this vector

in a standard x-y coordinate system?

1) 30°

2) 180°

3) 90°

4) 60°

5) 45°

ConcepTest 3.2b Vector Components II


A certain vector has x and y components

that are equal in magnitude. Which of the

following is a possible angle for this vector

in a standard x-y coordinate system?

1) 30°

2) 180°

3) 90°

4) 60°

5) 45°

The angle of the vector is given by tan q = y/x. Thus, tan q = 1

in this case if x and y are equal, which means that the angle

must be 45°.

ConcepTest 3.2b Vector Components II

Or 135º, 225º or 315º!


Motion in Three Dimensions

Chapter 3: Two Dimensional...

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