PHYS 201

Instructor : Dr. Hla

Class location: Walter 245

Class time: 12 – 1 pm (Mo, Tu, We, Fr)

Equation Sheet

You are allowed to bring an A4 size paper with your own notes (equations, some graph etc.) to the midterm and final exam. No equation will be given.

PHYS 201

Chapter 1

Power of TenUnitsUnit ConversionsBasic TrigonometryGraphical AnalysisVectorsVector Components

Prefixestera (T): 1012 1,000,000,000,000

giga (G) : 109 1,000,000,000

mega (M): 106 1,000,000

kilo (k): 103 1,000

centi (c): 10-2 1 / 100

milli (m): 10-3 1 / 1,000

micro (μ): 10-6 1 / 1,000,000

nano (n): 10-9 1 / 1,000,000,000

pico (p): 10-12 1 / 1,000,000,000,000

OU Atomic logo

30 nm

Basic UnitsSI CGS BE

Length [L] meter (m) centimeter (cm) foot (ft)

Mass [M] kilogram (kg) gram (g) slug (sl)

Time [T] second (s) second (s) second (s)

Dimensions

All the other units are derived units.Example: Speed can be expressed with mph (miles per hour, or mi / h). It is the unit of length divided by time (L / T).

Unit Conversion

Can't mix units when adding or subtracting - Need to convert

18 km + 5 mi is not 23

Can always multiply by 1

1 km =1000 m 1 = (1 km/1000m)

Can cancel units algebraically

Unit Conversion

Example 1Convert 80 mi to km.

Example 2Convert 60 mi/h to km/s, and m/s.

Example 3Convert 60 mi/h to ft/s.

1 mi = 5280 ft

1 mi = 1.609 km

1 m = 3.281 ft

Unit Conversion

Example 4

You are driving on R33 near Logan with a speed of 26.67 m/s. The speed limit there is 65 mph. Will you get a ticket because you are speeding?

Example 4

You are driving on R33 near Logan with a speed of 26.67 m/s. The speed limit there is 65 mph. Will you get a ticket because you are speeding?

Unit Conversion

Example 5

CLICKER!

Convert 1000. ft/min into meters per second.

1). 0.197 m/s2). 5.08 m/s3). 24.5 m/s4). 54.7 m/s5). 169 m/s6). 1540 m/s7). 18300 m/s

Convert 1000. ft/min into meters per second.1. 0.0847 m/s

2. 0.197 m/s

3. 5.08 m/s

4. 24.5 m/s

5. 54.7 m/s

6. 169 m/s

7. 1540 m/s

8. 18300 m/s

1 mi = 5280 ft

1 mi = 1.609 km

1 m = 3.281 ft

m/s08.5f281.3

m1

s60

min1

s

ft1000

t

ANSWER!

Unit Conversion

Example 6

CLICKER!

(1) 1.56x10-6 m3

(2) 1.56x10-4 m3 (3) 1.56x10-3 m3

(4) 1.56x10-2 m3

(5) 1.56x10-1 m3

(6) 1.56 m3

(7) 15.6 m3

(8) 1.56x103 m3

(9) 1.56x106 m3

(10) 1.56x109 m3

A bucket has a volume of 1560 cm3. What is its volume in m3?A bucket has a volume of 1560 cm3. What is its volume in m3?

A bucket has a volume of 1560 cm3. What is its volume in m3? (1) 1.56x10-6 m3 (2) 1.56x10-4 m3 (3) 1.56x10-3 m3

(4) 1.56x10-2 m3 (5) 1.56x10-1 m3 (6) 1.56 m3

(7) 15.6 m3 (8) 1.56x103 m3 (9) 1.56x106 m3

(0) 1.56x109 m3

1560cm3 = 1560 cm*cm*cm (1m/100cm)*(1m/100cm)*(1m/100cm)

= 1.56x10-3 m3

How do you interpret cm-3 ?

Negative exponent – inverse – place in denominator

3cm

1

ANSWER!

Trigonometry

• Right Triangle Sum of angles = 180

opposite angle = 90-θ

22oa hhh

Trigonometry

• Right Triangle

hypotenuse

oppositesin

hypotenuse

adjacentcos

adjacent

oppositetan

Which is true?

1. A = B + C

2. B = A – C

3. C = A + BB

CLICKER!

A

C

2 2 2

2 2 2

2 2 2

Which is true?

1. A = C sin

2. A = C cos

3. B = C cos B

CLICKER!

A

C

Example:

You walk a distance of 20m up to the top of a hill at an incline of 30°. What is the height of the hill?

Note: DRAW PICTURE!

30º

20mh

m 10

30sin m) 20(

m 20sin

h

h

h

o

What is the angle θ?

9.36

0.6

5.4tan 1

m

m

DIMENSIONS

Length: L

Mass: M

Time: T

Examples:

1). Speed: unit (mi/h). Dimension: [L/T]

2). Area : unit (ft2). Dimension: [L2]

3). Acceleration: Unit (m/s2). Dimension: [L/T2]

4). Force: Unit (kg. m/s2) . Dimension: [ML/T2]

DIMENSIONS

Length: L

Mass: M

Time: T

Dimensions of left and right side of an equation must be the same.

Example: x = ½ vt2

L = (L/T) (T2) = LT [Dimensions at left and right are not the same.WRONG equation.]

Example: x = ½ vt

L = (L/T) (T) = L [Dimensions at left and right are the same.CORRECT equation.]

You are examining two circles. Circle 2 has a radius 1.7 times bigger than circle 1. What is the ratio of the areas? Express this as the value of the fraction A2/A1.

(1) 1/1.7 (2) 1.7 (3) (1/1.7)2 (4) 1.72

(5) (6) 7.1/1 7.1

22

1

21

21

22

1

2 )7.1()7.1(

r

r

r

r

A

A

2rA

Example:

12

CLICKER!

Slope of Function on Graph

• Slope = rise/run• Up to right is positive

• Slope of curve at a point– slope of tangent line

• Slope of straight line same

at any point

x

y

run = Δx

rise = Δy

x

y

A

The slope at point B on this curve is _________ as you move to the right on the graph.

1. increasing

2. decreasing

3. staying the same

x

y

B

CLICKER!

The slope at point B on this curve is _________ as you move to the right on the graph.

1. increasing

2. decreasing

3. staying the same

x

yB

CLICKER!

The slope at point B on this curve is _________ as you move to the right on the graph.

1. increasing

2. decreasing

3. staying the same

x

y

B

Vectors

Vectors

Direction

length = magnitude

Some VECTOR quantities

-Displacement (m, ft, mi, km)-Velocity (m/s, ft/s, mi/h, km/hr)- Acceleration (m/s2, ft/s2)-Force (Newton, N)

Vector Summation

+ =A B C

+ =A B C

Vector Summation

AB

A BC = +

1) 2)

+

Two ways to sum the vectors: Parallelogram method (1), and triangle method (2).

Vector Summation

A

BC

C = A + B

2 2

= tan

A

B-1

Which is true?

CLICKER!

A

B

A BC = +

1)

2)

3)

4)

Which is true?

CLICKER!

AB

A BC = +

1)

2)

3)

4)

Vector Component

A

A

A

Y

x

x

Y

Example

40 N

30 N

60

An object is pulled by strings with 30 N and 40 N forces respectively as shown. Find (a) the magnitude of the net force. (b) the direction of the net force (find the angle).

CAPA

- Round up the numbers (e.g. 3.247321 3.25)

-Add the units: (e.g. cm, N (newton), deg (degree))

-Do not forget to put ‘-’ sign in vectors if the resultant vector is in –x or –y direction.

-For m/s2 m/s^2