Ok, this problem has been driving me crazy. I was thinking that the force is zero since the magnitude of the angular acceleration is zero, however that is not the case.

Do you know that the acceleration of the centre of mass of a rigid body is equal to
(The net extenal force)/The total mass ? ( That's what the hint implied).
If you apply this theorem to the blade,the force will be (Total mass)*( The acc. of the centre of mass, which is L/2 into the angular speed squared).
I am, with great respect,
Einstone.
P.S.- Angular acceleration results only in case of an external torque.