A Humbling Moment

All objects are mutually attracted
– Accelerate at 10m/s^2

The Train… of Pysics!
What trajectory would the apple follow?

In physics motion at constant speed is indistinguishable from being at rest!

F:10N
time:4.47sec
acceleration:1 m/s^2

Δx=v0t+1/2at^2
10m = 0 + 1/2a(4.47)^2

N = Normal(perpendicular)
FN mg=weight, mg is equal to FN

Forces and trig
if α=30°、Fr=100N sin(30degree)*100
FRX = 50N, Fry = 86.6N cos(30degree)*100

m = 10Kg
mg = 100N
Fry = 50N
Fn = 150N
Frx = 86.6N
Fw = 86.6N

Components of Motion

2-D motion can be solved as two
1-D motion problems

Δx = V0t + 1/2αt^2
V = V0 + at
V^2 = V0^2 + 2αΔx

Δox = 10m/s
α- 10m/s^2

Dimensional Analysis
E = mc^2, E = M*L*T

Experiment, Evidence Rules, Motion Equation
1D/ 2D ΔX = v0t + 1/2at^2

Explain the cause of motion
Understand “rest”

the motions of stars and apples have in different, but governed by same laws

Why learn about motion?

Kinematics
1. predictive power
2. important tool
3. solve nature’s puzzle

Galileo Galilei:object fall at constant speed
Aristotle vs Galileo: objects gain speed as they fall

A mass dropped from greater height leaves greater impact
Feathers do fall at constant speed
Air slows objects down! … too fast

Position, Velocity
Velocity: v = Δx / Δt
Acceleration a = ΔV / Δt

v = 5m / 1s = 5 m/s

Average deviation
2.00m, 1.20m, 2.80m -> 1.6/3 => 0.53
1.97m, 1.98m, 1.97m -> 0.02/3 => 0.0067
m / s / s
“constant acceleration means an object gains equal speed during equal time intervals”
Vαt^2
x = t^2, a = 10m/s^2 = g
V0 = 10m/s

latitude

latitude
https://www.esrl.noaa.gov/gmd/grad/solcalc/

Shadows and Trigonometry
18m, 10m, β
β = arctan(18/10) in degrees = 60.9°

w = 25m / tan(1.3°) = 1101m

MC = 40,000Km / 3.68, MC = 10,900K

distance to the moon
10900 = πd
d = 3470km
tan(0.5°)=3470 / L
L = 3470 / tan(0.5) = 398,000 km

distance to the sun
cos α = 400,000/L
L = 400,000/ cos89.853°
L = 156,000,000 km

trigonometric ratios

tan, sin, cos
e.g. tanα = 231 /266

using angle table
534.6m, 401.0m

length of bar = 1.00m, length of shadow = 0.126m, α = 7.2°

Eratosthenes vs Reality
try out in Google
cos(44 degrees) = 0.7193319

reverse tangent -> arctan(0.932) in degrees -> 42.98
sin(30 degree) = 0.5
tan(79 degree) = 5.14
arcsin(0.62) in degrees = 38.32°
arctan(4/7) in degrees = 29.74°
arctan(1/40) in degrees = 1.42°

α = 7.2°+- 1.4°
αmin = 5.8°, C = 57,400km
αmax = 8.6°, C = 46,250km

Landmark of physics

Eratostheness

How long the earth’s circumstance?
Geometry sun’s position

Plato “The earth’s circumference is 400,000 stadia.”
≒ 74,000
1 stadium = 185m

True Circumference is 40,000 Km
Plato’s guess was 85% larger than the true circumference.

Archimedes: circumference of Earth is 300,000 stadia
Archimedes: Look at the geometry of a sphere and find a clever way to calculate the circumference

Delegation

AVAudioRecorder
Record VC

func audioRecorderDidFinishRecording(_ recorder: AVAudioRecorder, successfully flag: Bool){
	if flag {
		performSegue(withIdentifier: "stopRecording", sender: audioRecorder.url)
	} else {
		print("recording was not successful")
	}
}

override func prepare(for segue: UIStoryboardSegue, sender: Any?){
	if segue.identifier == "stopRecording"{
		let laySoundsVC = segue.destination as! PlaySoundsViewController
		let recordedAudioURL = sender as! url
		playSoundVC.recordedAudioURL = recordedAudioURL
	}
}

Stack Views: Horizontal, Vertical
-alignment, distribution, spacing

AVAudioEngine

var dollars:Int = 10
var cents:Int = 50
var amount = "$\(dollars).\(cents)"
print(amount)

dollars = 19
centsd = 99
amount = "$\(dollars).\(cents)"
print(amout)

func printMoneyString(dollars:Int, cents:Int){
	print("$\(dollars).\(cents)")
}

Tour of Xcode

Document Outline in Xcode

Model View Controller
view(UIView, UILabel, UIButton), controller, model

AutoLayout Basics

@IBOutlet weak var recordButton: UIButton!
@IBOutlet weak var recordingLabel: UILabel!
@IBOutlet weak var resumeButton: UIButton!
@IBOutlet weak var resumeLabel: UILabel!
@IBOutlet weak var pauseButton: UIButton!
@IBOutlet weak var pauseLabel: UILabel!
@IBOutlet weak var stopButton: UIButton!
@IBOutlet weak var stopLabel: UILabel!

@IBOutlet func recordButtonPressed(sender: UIButton){
	// ...
}

ViewController and Multiple Views
Not Running, Inactive, Active, Background, Suspended

Audio in iOS
Pitch Perfect App, AVFoundation, Core Audio, Audio Hardware

import AVFoundation

class ViewController: UIViewController {
	var audioRecorder: AVAudioRecorder!

	@IBAction func recordAudio(_ sender: AnyObject){
		recordingLabel.text = "Recording in progress"
		stopRecordingButton.isEnabled = true
		recordButton.isEnabled = false

		let dirPath = NSSearchPathForDirectoriesInDomains(.documentDirectory,.userDomainMask, true)[0] as String
		let recordingName = "recordedVoice.wav"
		let pathArray = [dirPath, recordingName]
		let filePath = URL(string: pathArray.joined(separator: "/"))

		let session = AVAudioSession.sharedInstance()
		try! session.setCategory(AVAudioSessionCategoryPlayAndRecord, with:AVAudioSessionCategoryOptions.defaultToSpeaker)

		try! audioRecorder = AVAudioRecorder(url: filePath!, settings: [:])
		audioRecorder.isMeteringEnabled = true
		audioRecorder.prepareToRecord()
		audioRecorder.record()
	}
}