FYKOS Year 33 Series 2 Problem 5 — wheel with a spring · FYKOS 33 #33.2.5
Physics · mechanics
Problem
We have a perfectly rigid homogeneous disc with a radius R and mass m, to which a rubber band is connected.
It is fixed by one end in distance 2R from an edge of the disc and by the other end at the end of the disc.
The rubber band behave as ideal, thin spring with stiffness k, rest length 2R and negligible mass.
Disc is secured in the middle, so it is able to rotate in one axis around this point, but cannot move or change the rotation axis.
Figure out relation between the magnitude of moment of force, by which the rubber band will be increasing or decreasing the rotation of
disc depending on ϕ. Also, figure out an equation of motion.
Bonus Define the period of system's small oscillations.