Applying Rotational Dynamics to a Childrens Show About Colorful Ponies.
So I have a test on Circular Motion in physics coming up on Monday, and I thought "What better way to study then apply what I learned to MLP:FIM?"
Well, many of you may remember this scene from "wonderbolts academy"
http://www.youtube.com/watch?v=kpyDq0nIWuM
Well through some observations I calculated various values relating to the circular motion of the pony (Wildflower according to the internet).
Here is my work on paper
Front:
Back:
So without further ado here is my explanation:
Based on observation and a educated guess that the length of an outstreched pony is about 4ft I found the distance from the dizzitron to Wildflowers COM to be about 1.5 pony lengths or about 1.83m.
Another educated guess, I assumed the average adult pegasi probalby weight about 60lb or 27.22 Kg.
At maximum angular velocity Wildflower makes 1 rotation about every 1 seccond about the dizzitron making her final angular velocity to be about 6.28 rad/s.
The time required for the dizzitron to reach maximum angular velocity came out to be about 6 secconds.
Finally, Wildflowers moment of inertia, without counting the dizzitron itself plugged into the formula I=mr^2 came out be about 91.16 Kg * m^2
Based on this I was able to find angular acceleration, Tangential Velocity, Radial Acceleration, Centripetal Force, Torque, Angular Momentum, and finally Rotational Kinetic Energy.
Now, the calculations.
Angular Acceleration
α = ωf - ωi / t
since intitial angular velocity is zero we get
α = 6.28rad/s / 6s
α = 1.047 rad/s^2
Tangential Velocity:
VT = ωf * r
VT = 6.28 rad/s * 1.83
VT = 11.49 m/s
Radial Acceleration
aR = (VT)^2 / r
aR = (11.49m/s)^2 / 1.83m
aR = 72.14 m/s^2 = 7.36 g's
Centripetal Force
Fc = mwf * aR
Fc = (27.22 Kg)(72.14 m/s^2)
Fc = 1963.65 N
Torque on Wildflower
T = I * α
T = (91.16 Kg * m^2) * (1.047 rad/s^2)
T = 95.44 m * N
Angular Momentum of Wildflower
L = I * ω
L = (91.16 Kg * m^2) * (6.28 rad/s)
L = 572.76 (Kg * m^2)/ s
Rotational Kinetic Energy of Wildflower
KE = (1/2) I * ω^2
KE = (1/2)(91.16 Kg * m^2) * (6.28 rad/s)^2
KE = 1797.60 J
Studying with ponies is the only way to study.
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