i mean that because the circumference changes and the radius does not, this means that the angle θ changes. With a full disk, θ=2π, so the circumfrence, which is the same as the arc length of a full circle, is 2πrγ, but then if r does not change, then θ changes. For a full disk, when v=0, then θ=2π, but when v does not equal 0, then θ=2πγ. This means that part of it gets cut off and the angle it makes is 2πγ. But we are also forgetting that it depends on relative velocities. What are relative velocities like with angular motion?