There was a bit of discussion of this, as alluded to above, at
http://www.pprune.org/tech-log/43276...ml#post6049727.
I guessed values that were tweaked by others on that thread.
For the updated values of a 75kg, 1.1-m diameter disk at 10,000 rpm, kinetic energy is up to 8MJ (same as a 15-ton truck at 70mph). The shafts have a small contribution - it's the wide-radius parts that dominate.
The fan is heavier and bigger, and so makes a greater contribution to the energy of rotation in the engine [dependent on mass * (radius * angular speed)**2]. Assuming four times the mass, twice the radius, and a third of the speed, the fan would have about twice the rotational kinetic energy of a turbine disk.
The fan is even more dominant in the gyroscopic effect [dependent on angular momentum, scaling as (mass * radius**2 * angular speed)], exceeding the contribution of the turbine disks by a factor of 5. As ChristiaanJ says above, gas-flow efficiency considerations are probably the most important for deciding on contrarotating IP and HP sections, not reducing the fan-dominated gyroscope effect.