Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this...

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DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

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Transcript of Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this...

Page 1: 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

Page 2: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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

Page 3: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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.

Page 4: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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.

Page 5: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

International-Mindedness

Vector notation forms the basis of mapping across the globe

Page 6: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Theory Of Knowledge

What is the nature of certainty and proof in mathematics?

Page 7: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Understandings

Vector and scalar quantities Combination and resolution of

vectors

Page 8: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Applications And Skills

Solving vector problems graphically and algebraically

Page 9: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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

Page 10: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Data Booklet Reference

Page 11: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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)

Page 12: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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

Page 13: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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

Page 14: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Introductory VideoWhat are scalars and vectors?

Page 15: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Scalars

Require only a number to represent them

No direction involved

Page 16: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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

Page 17: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Examples of Vectors and Scalars

Page 18: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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

only affects the magnitude and not the direction

3xA

Page 19: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Introductory VideoAdding Vectors

Page 20: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Adding VectorsParallelogram Method

A

B

R

Page 21: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Adding VectorsHead-To-Tail Method

A

B

R

Page 22: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Subtracting VectorsHead-To-Tail Method

A

B

R

Page 23: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Adding VectorsHead-To-Tail by ComponentsA

B

R

Page 24: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Adding VectorsHead-To-Tail by ComponentsA

B

R

R

xR

yR

Page 25: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Adding VectorsHead-To-Tail by ComponentsA

B

R

A

xA

yA

B

xB

yB

Page 26: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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

Page 27: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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

Page 28: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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

Page 29: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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

Page 30: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Adding VectorsComponent Method

R

xR

yR

o

x

y

x

y

R

R

R

R

8.17

2.39

6.12tantan

tan

11

Page 31: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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.

Page 32: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Understandings

Vector and scalar quantities Combination and resolution of

vectors

Page 33: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Applications And Skills

Solving vector problems graphically and algebraically

Page 34: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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?

Page 35: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

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?

Page 36: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

QUESTIONS?

Page 37: Essential Idea Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation.

Homework

#1-16


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Math Review Scalar Quantities: (Magnitude only) Mass Mass Volume Volume Density Density Speed Speed Vector Quantities (Magnitude and direction) Force Force.

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Projectile Motion Chapter 3. Vector and Scalar Quantities Vector Quantity – Requires both magnitude and direction Velocity and Acceleration = vector quantities.

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