Mechanics of the YoYo

1 / 16

# Mechanics of the YoYo - PowerPoint PPT Presentation

Mechanics of the YoYo. Rotational & Translational Energy. Seth T Chase. Understand Energy in Motion. Energy of any particle is constant Kinetic (T) + Potential (U) = Constant (E) U = mgh K = 2 mv 2 + 2 I ω 2 I = 2 mr 2 ω 2 E = mgh + 2 mv 2 + 3 mr 2 ω 2. Goals.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Mechanics of the YoYo' - dori

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Mechanics of the YoYo

Rotational & Translational Energy

Seth T Chase

Understand Energy in Motion
• Energy of any particle is constant
• Kinetic (T) + Potential (U) = Constant (E)
• U = mgh
• K = 2mv2 + 2Iω2
• I = 2mr2ω2
• E = mgh + 2mv2 + 3mr2ω2
Goals
• Derive formula translational acceleration
• Apply Euler algorithm to create relationships of motion and apply Leapfrog algorithm method to update visual
• Relate rotational motion to derived formula for translational motion
• Show energy is conserved by calculating forces within code
Euler & Leapfrog Algorithm

Creating Motion due to Gravity

yoyoAccCM = ((2.0/3.0)*9.81)

yoyo.acceleration = yoyoAccCM * vector(0,-1,0)

yoyo.velocity.y = yoyo.velocity.y + yoyo.acceleration.y*dt

yoyo.pos = yoyo.pos + yoyo.velocity*dt + yoyo.acceleration*dt*dt*0.5

Changing Direction

yoyo.velocity.y = -yoyo.velocity.y - yoyo.acceleration.y*dt

Translational & Rotational

Determining Angular Velocity (ω)

w = yoyo.omega*direction

Rotating Frame on Changing Position

ypos = yoyo.pos.y

Calculating Forces

Total Energy

Energy = (Potential + Kinetic) -(Energy*dt)

Kinetic Energy

K1 = Kinetic

K2 = Kinetic

Potential Energy

P1=Potential

Potential = -(yoyo.mass*yoyoGravCM*(8.8-yoyo.pos.y+ changeINposition))

P2=Potential

• Introduction to frames
• Scenes and there benefits
• Adding visual components of Energy Conservation
Frames and their use

Creating Frames

lever=frame(pos=(2,0,0))

yoyo=frame(pos=(0,8.8,0))

Connecting Frames

middle_left=cylinder(frame=yoyo, pos=(0,0,0),

Creating a Scene vs. Conditional statements

Creating Scene

scene.width = 1000

scene.height = 1000

scene.center = (0,5.5,0)

Creating Objects with Variable Components

mass1 = box(pos=(3.5,12.5,.2) ,length=.6, height=.6, width=.6,color=color.red)

mass1.mass = .005

message = "Click to add 1.0 gram."

mass1Label = label(pos=(4,12.3,.2), text=message,xoffset=20)

Detecting and Implementing Mouse Click

if scene.mouse.events: # detect mouse events

mouse = scene.mouse.getclick()

if mouse.pick == mass1 or mouse.pick==mass2:

Sliding Bars of Kinetic & Potential Energy

Creating Boxes and Bars

PBar = box(pos=(5.5,6.65,.1), length=.9, height=.1, width=.9)

PBox=box(pos=(5.5,6.465,0),length=1, height=1.34, width=1, color=color.red)

message = "Potential Energy"

PboxLabel = label(pos=(4.9,6.7,0),text=message,xoffset=-17)

Updating Bars to Move in Box

PBar.pos.y = (PBox.pos.y+(PBox.height/2)-(PBar.height/2))- ((PBox.height*(P2/P_mag))/(2*handle.pos.y))

Problems within Code
• Bouncing at same height
• Eliminating errors by increasing rate and decreasing dt
• Finding right proportions of position change when increasing mass and showing via thickness