The rotational energy or angular kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation, one gets the following dependence on the object's moment of inertia:

**E = ½mv²**
Where E is the kinetic energy, m is the mass, and v is the velocity.

The mechanical work required for inertia applied during rotation is the torque times the rotation angle. The instantaneous power of an angularity accelerating body is the torque times the angular velocity. For free-floating (unattached) objects, such as a staff, the axis of rotation is commonly around its center of mass.

We have not seen any limit for how long Hiruzen's staff can extend, so in theory we can write:

**0 < x < ∞∀ ℝ**
Where x = the size of Hiruzen's staff.

As Hiruzen's staff increases in size, the mass, m, of the object tends to infinity and hence the kinetic energy, E, also tends to infinity.

The amount of energy required to destroy the Earth is 210,000,000,000,000,000,000 joule. Assuming that Hiruzen drops his staff (velocity = 9.8m/s due to gravity), then the mass of his staff would need to be 4,373,177,842,565,600,000 kilograms.

And because 4,373,177,842,565,600,000 < ∞ , it follows that x, the size of Hiruzen's staff, can also equal 4,373,177,842,565,600,000.

Conclusion: