b. Now suppose the ant walks with speed v along a circle of radius r, tangent to its starting point.
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Through what net angle does the disk rotate?
Given constants:
## Disk Jockey
A disk of uniform mass density, mass M, and radius R sits at rest on a frictionless floor. The disk is attached to the floor by a frictionless pivot at its center, which keeps the center of the disk in place, but allows the disk to rotate freely. An ant of mass m≪M is initially standing on the edge of the disk; you may give your answers to leading order in m/M.
Context question:
a. The ant walks an angular displacement θ along the edge of the disk. Then it walks radially inward by a distance h≪R, tangentially through an angular displacement −θ, then back to its starting point on the disk. Assume the ant walks with constant speed v.
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Through what net angle does the disk rotate throughout this process, to leading order in h/R ?
Context answer:
M2mθ((1−Rh)2−1)