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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.

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mechanics of the yoyo

Mechanics of the YoYo

Rotational & Translational Energy

Seth T Chase

understand energy in motion
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
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
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.omega*yoyo.radius_string

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

translational rotational
Translational & Rotational

Determining Angular Velocity (ω)

yoyo.omega =(yoyo.velocity.y/yoyo.radius_string)

w = yoyo.omega*direction

Rotating Frame on Changing Position

ypos = yoyo.pos.y

yoyo.rotate(angle=(radians(w)), axis=(1,0,0), origin=(0,ypos,0))

calculating forces
Calculating Forces

Total Energy

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

Kinetic Energy

K1 = Kinetic

Kinetic =(.5*yoyo.mass*yoyo.velocity.y**2)+ (.25*yoyo.mass*(yoyo.omega*yoyo.radius_spin)**2)

K2 = Kinetic

Potential Energy

P1=Potential

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

P2=Potential

additional remarks on code
Additional Remarks on Code
  • Introduction to frames
  • Scenes and there benefits
  • Adding visual components of Energy Conservation
frames and their use
Frames and their use

Creating Frames

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

handle=arrow(frame=lever,pos=(0,10,0),axis=(- 2,0,0),radius=.01)

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

Connecting Frames

left_side=ring(frame=yoyo, pos=(-.50,0,0), axis=(1,0,0),radius=yoyo.radius_ring, length=2.5,thickness=0.3,color=color.yellow)

top_left_ball=sphere(frame=yoyo, pos=(-0.7,0.8,0), radius=0.2, color=color.blue)

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

axis=(-.5,0,0),radius=yoyo.radius_spin, color=color.green)

creating a scene vs conditional statements
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:

right_side.radius += mouse.pick.mass

sliding bars of kinetic potential energy
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
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