01 - review of vectors and scalars

7/29/2019 01 - Review of Vectors and Scalars

1/24

Review of Vectors andScalars; Scientific Notation

and Units

Ms. Mikaela Fudolig

Physics 71 EEE


2/24

Review: Vectors and Scalars

Scalars magnitude only

Vectors magnitude and direction

Scalar representation: number + unitsVector representation

Arrows

Unit vectors


3/24

Scalar addition

Scalar + Scalar (never Scalar + Vector)

Scalars must have the same units before

you can add them (never kg + mL)

How to add: just add arithmetically


4/24

Vector addition: Graphical

representation

Tail-to-head

A

B


5/24


representation

Tail-to-head

A

BC


6/24


representation

Tail-to-head

A

B

C


7/24

Scalar-Vector Multiplication

Scalar x Vector

Magnitude changes (length of arrow)

Direction:

Scalar > 0: Direction REMAINS THE SAME

Scalar < 0: Direction REVERSES


8/24

Vector Subtraction: Graphical

representation

Similar procedure as in vector addition

Technique:

Reverse direction of the vector to be subracted:

( 1)A A


9/24

Unit Vectors

Vectors are expressed as a combination of

unit vectors

- one vector of length 1 in the +x direction - one vector of length 1 in the +y direction

- one vector of length 1 in the +z direction

i

j

k


10/24

Vector Addition

Add the is to the is, the js to the js, and

the ks to the ks.

Arithmetic

Do NOT add the is to the js, etc.


11/24

Scalar-Vector Multiplication

Multiply ALL components by that scalar

. 2( 4 ) 2 8ex i j i j


12/24

Converting from graphical to analytic

Trigonometry!

Never forget:

SOHCATOAPythagorean theorem


13/24

Exercise 1

A vector has a length of 3 units and is

directed 30 north of west. Express this

vector in terms of the unit vectors i, j, and

k. Assume that north points in the +jdirection.


14/24

Exercise 2

A vector has a length of 3 units and is

directed 30 west of north. Express this

vector in terms of the unit vectors i, j, and

k. Assume that north points in the +jdirection.


15/24

Exercise 3

Consider the displacement vector:

How long is this vector, and in what

direction does it point?

3m 2 mi j


16/24

Exercise 4

Give the resultant of the following vectors:

3m 2 mA i j

5m 2 m 3mB i j k


17/24

Units and Scientific Notation

Units are important to know the amount of

a quantity (scalar or vector).

Meter vs. foot

Gram vs. kilogram

I weigh 100. (what?)


18/24

Converting Units

Dimensional Analysis

Involves multiplying quantities by a factor of 1

?

5.00 1

ft

cm cm

1 15.00

? 12

in ft cm

cm in

1 15.00

2.54 12

in ft cm

cm in


19/24

Significant figures

All nonzero digits are significant.

All zeroes between significant figures are

significant.

If a whole number ends in a zero and

there is no decimal point after it, the digit

0 is not significant. (ex. 100 vs 100.)

A 0 is significant if it is trailing, not if it is

leading (ex. 0.010)


20/24

Scientific Notation and SF

Using scientific notation makes it easier to

identify SF

1.30 x 103 g vs. 1300g


21/24

Exercise

How many SF are there?

100.20 m

0.01050 g

10030 cm

500.0 m

2.050 x 103 J


22/24

Operations with SF

Addition/Subtraction

SF after the decimal place is what is important

SF post-decimal place of Sum/difference must

be the same as the post-decimal place SF ofthe addend/subtrahend with the smallest post-

decimal place SF

Ex. 100.15 + 10.2 = 110.35 110.4

expressed in scientific notation, express them

with the same exponent, then add.


23/24

Operations with SF

Multiplication/Division

Product/Quotient must have the same SF as

the factor/divisor/dividend the smallest SF

Ex. 100 x 25.0 = 2500 3000


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Operations with SF

If you have more than one arithmetic

operation, do NOT use the SF rules to

round up or down!

Ex. 120.0 + 55 x 10 = 120.0 + 550 = 670

not 120.0 + 600

Ex. 120.0 + 55.0 x 100.0 = 1.200 x 102 + 5.50 x

102 = 6.70 x 102

01 - review of vectors and scalars

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