Turns out, you have access to a high-powered water hose of the kind typically used to fend off boar tigers! This may come in handy, as the rotating platform of the generator has small little cups which would act perfectly to catch water. The cups line the platform at a distance $r_{0}=2.5\,{\rm m}$ from the center, and the hose can generate a constant force $F_{0}=200\,{N}$.
In order to prove to Aunt Entity that this high-powered water hose is a much better approach to power the generator – since she cannot follow your mathematical acrobatics – you must produce a visual display of the angular momentum vector to demonstrate that the platform does indeed begin to speed up quickly.
But not too fast! As luck would have it, your water supply is limited! Determine how long it will take for the generator to ramp up to the required kinetic energy, using Python's graphing capabilities.
Attached below are the remnants of crazy Dr. Wiley's attempt at a simulation, however he just could not finish the job. Take up where he left off!
First, we need to assume that the torque delivered by the hose is a constant:
I = (1/2)*300*(2.5**2) L = 0 F = 200 r = 2.5 tauhose = r*F
The $\tau_{\rm hose}$ can go in the parameters section since it doesn't depend on time, or it could go in the calculation loop. Either one will work, but you should ask if it is time dependent or not. Then, we need to update the angular momentum in the calculation loop by adding the net torque and the angular momentum update:
taunet = tauhose L = L + taunet*dt
At this point, they can uncomment out the Larrow and add in the graph give and give it the proper attributes:
Larrow = arrow(color=color.orange) EnergyGraph = PhysGraph(1) Larrow.pos = axel.pos Larrow.axis = vector(0,L/100,0) graph.plot(pos=(t,(1/2)*I*(L/I)**2))
With these numbers, from the graph, the time in order to achieve the necessary kinetic energy is $t_{\rm frictionless}\approx 2.7\,{\rm s}$.
Given that this method produces an angular momentum and kinetic energy that increases to infinity, we should prompt them to add in a torque due to friction (see tutor question below).
b = 0.00025 taufric = -b*L**2 taunet = tauhose + taufric
https://www.glowscript.org/#/user/pcubed/folder/solutions/program/SpinMeAroundSolution
#Imports from __future__ import division from visual import * from physutil import * #Objects axel = cylinder(pos=vector(0,-5,0), axis=vector(0,0.5,0), radius=0.1, color=color.white) platform = cylinder(pos=vector(0,-5,0), axis=vector(0,0.1,0), radius=10, material=materials.marble) #Parameters and Initial Conditions I = (1/2)*300*(2.5**2) L = 0 F = 200 r = 2.5 b = 0.00025 #Time and time step t=0 tf=10 dt=0.01 #MotionMap/Graph Larrow = arrow(color=color.orange) EnergyGraph = PhysGraph(1) #Calculation Loop while t < tf: rate(100) taufric = -b*L**2 tauhose = r*F taunet = tauhose + taufric L = L + taunet*dt platform.rotate(angle=(L/I)*dt, axis=vector(0,1,0), origin=axel.pos) EnergyGraph.plot(t, (1/2)*(1/I)*(L)**2) Larrow.pos = axel.pos Larrow.axis = vector(0,L/100,0) t = t + dt