p86. A rod on a low friction axle is initially at rest when a constant torque begins to be applied (a) complete the skeleton program shown below and make sure that it runs properly. See Section 11.10 for suggestions. After exiting the loop, print the values of the final angle theta and the final angular speed mag(omega). Given the fact that the torque is constant, what should be the value ratio mag(omega)/theta? Is this true for your program?

# M+I P86, Angular Momentum principle

from __future__ import division , print_function from visual import * from visual.graph import *

M=2 Lrod = 1 R = 0.1 Laxle = 4*R I = (1/12)*M*Lrod**2 + (1/4)*M*R**2

rod = cylinder(pos=vector(-1,0,0),radius=R, color=color.orange ,axis=vector(Lrod ,0 ,0) ) axle = cylinder(pos=vector(-1+Lrod/2,0,-Laxle/2) ,radius=R/6, color=color.red, axis=vector(0 ,0 ,4*R) ) L = vector(0 ,0 ,0) # angular momentum dt = 0.0001 # for accuracy in later parts t=0 theta = 0 dtheta = 0 omega=L/I

axis_of_rotation = vector(0 ,0 ,1) while t < 6: rate (1000) torque = vector(0 ,0 ,2) # constant torque # Apply Angular Momentum Principle, in update form # missing code: fill in ....

# Update angle and rod position omega = L / I omega_scalar = omega.z dtheta = omega_scalar * dt # rotate the rod with new angle rod.rotate(angle=dtheta , axis=axis_of_rotation ,origin=axle.pos) theta = theta + dtheta # Update time (ie increment time in while loop... see other code you're written) # missing code: fill in ....

# print output asked for, after while loop # missing code: fill in ....