Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

DEVIL PHYSICSTHE BADDEST CLASS ON

CAMPUSIB PHYSICS

TSOKOS LESSON 1-4IB TOPIC 1-3VECTORS AND SCALARS

Essential Idea

Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation of quantities. This sub-topic will have broad applications across multiple fields within physics and other sciences.

Nature Of Science

Models: First mentioned explicitly in a scientific paper in 1846, scalars and vectors reflected the work of scientists and mathematicians across the globe for over 300 years on representing measurements in three-dimensional space.

International-Mindedness

Vector notation forms the basis of mapping across the globe

Theory Of Knowledge

What is the nature of certainty and proof in mathematics?

Understandings

Vector and scalar quantities Combination and resolution of

vectors

Applications And Skills

Solving vector problems graphically and algebraically

Guidance

Resolution of vectors will be limited to two perpendicular directions

Problems will be limited to addition and subtraction of vectors and the multiplication and division of vectors by scalars

Data Booklet Reference

Utilization

Navigation and surveying (see Geography SL/HL syllabus: Geographic skills)

Force and field strength (see Physics sub-topics 2.2, 5.1, 6.1 and 10.1)

Vectors (see Mathematics HL sub-topic 4.1; Mathematics SL sub-topic 4.1)

Objectives

Describe the difference between vector and scalar quantities and give examples of each

Add and subtract vectors by a graphical technique, such as tail-to-head or parallelogram rule

Objectives

Find the components of a vector along a given set of axes

Reconstruct the magnitude and direction of a vector from its given components

Solve problems with vectors

Introductory VideoWhat are scalars and vectors?

Scalars

Require only a number to represent them

No direction involved

Vectors

Cannot be fully specified without both a number (magnitude) and direction

Represented by an arrow from left to right over the variable

Two vectors are equal only if both their magnitude and direction are the sameA

Examples of Vectors and Scalars

Multiplying a Vector by a Scalar Multiplication of a vector by a scalar

only affects the magnitude and not the direction

3xA

Introductory VideoAdding Vectors

Adding VectorsParallelogram Method

A

B

R

Adding VectorsHead-To-Tail Method

A

B

R

Subtracting VectorsHead-To-Tail Method

A

B

R

Adding VectorsHead-To-Tail by ComponentsA

B

R

Adding VectorsHead-To-Tail by ComponentsA

B

R

R

xR

yR

Adding VectorsHead-To-Tail by ComponentsA

B

R

A

xA

yA

B

xB

yB

Trigonometry Revisited

A

BC

x

y

A

Bx

A

B

adj

oppx

C

Ax

C

A

hyp

adjx

C

Bx

C

B

hyp

oppx

o

o

o

1

1

1

tan,tan

cos,cos

sin,sin

45

Adding VectorsComponent Method

A

A

xA

yA

2.2145sin30

3045sin

2.2145cos30

3045cos

from45,30

oy

yo

ox

xo

o

A

A

A

A

xA

Adding VectorsComponent Method

B

B

xB

yB

5.825sin20

2025sin

1.1825cos20

2025cos

from25,20

oy

yo

ox

xo

o

B

B

B

B

xB

Adding VectorsComponent Method

R

xR

yR

2.41

6.125.81.21

2.391.181.21

22

222

yx

yyy

xxx

RRR

cba

BAR

BAR

Adding VectorsComponent Method

R

xR

yR

o

x

y

x

y

R

R

R

R

8.17

2.39

6.12tantan

tan

11

Essential Idea

Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation of quantities. This sub-topic will have broad applications across multiple fields within physics and other sciences.

Understandings

Vector and scalar quantities Combination and resolution of

vectors

Applications And Skills

Solving vector problems graphically and algebraically

Summary: Can you

describe the difference between vector and scalar quantities and give examples of each?

add and subtract vectors by a graphical technique, such as tail-to-head or parallelogram rule?

Summary: Can you

find the components of a vector along a given set of axes?

reconstruct the magnitude and direction of a vector from its given components?

solve problems with vectors?

QUESTIONS?

Homework

#1-16