[smallnamespace]

The platter is a circle so using the uniform distribution [0, 1] is incorrect, you should use the unit circular distribution of [0, 2pi] and also since the platter also spins in a single direction the distance is only computed going one way around (if target is right before current, it's one full spin).

But you can simplify this problem down and ask: with no loss of generality, if your starting point is always 0 degrees, how many degrees clockwise is a random point on average, if the target is uniformly distributed?

Since 0-180 has the same arc length as 180-360 then the average distance is 180 degrees. So average half-platter seek is half of the full-platter seek.

[Const-me]

What you wrote only applies to rotational latency, not seek latency. The seek latency is the time it takes for the head to reach the target. Heads only rotate within the small range like [ 0 .. 25° ], they are designed for rapid movements in either direction.