How do we know it is the Centripetal Force we have to calculate? A helicopter rotor blade is 7.80 m long and has a mass of 110 kg. (a) What force is exerted on the bolt attaching the blade to the rotor axle when the rotor is turning at 320 rev/min? (Hint: For this calculation the blade can be considered to be a point mass at the center of mass. Why?
 A: There are actually three important components of the bolt force: vertical, to keep the blade from falling, horizontal-tangential which pushes or pulls on the blade perpendicular to its length, and horizontal, to keep the blade from flying away from the rotor axle.
In order to calculate the vertical force you would need to know the shape and size of the fulcrum that keeps the blade level. Since that isn't given to you, you can't calculate a number. One could make a statement like "if the bolt is $x$ meters from the end of the support structure to which the blade is attached" you could express the vertical force in terms of $x$. I doubt that is what the question intends for you. Also, we don't know anything about the lift exerted on the blade, nor the weight of the helicopter.
To calculate the horizontal-tangential you would need to know air resistance and whether the blade is increasing, decreasing, or constant in rotational speed. There's not enough information to calculate this.
Your only remaining choice is the horizontal force. Because the motion of the blade is circular, that force must be providing the centripetal acceleration for the blade to move on that non-linear path.
So $$\sum \vec{F} = m\vec{a_c} = m\omega^2 r (-\hat{r}) $$
A: As said in the question, we can consider the blade as a point mass.
Now don't imagine that the blades are connected to the axle, rather think of them as the mass of the blade tied to a string 7.80 m/ 2 (distance of the center of mass and the axle) from the axle. Now, when the masses move in a circular motion the only thing that is keeping them moving in a circle is the centripetal force (in this case it's the tension of the string that we assumed).
An equal and opposite force would be acting on the axle (Tension acts equal and opposite to connected masses). That's how we know we have to find out the centripetal force.
I am not so knowledgeable in this field but this is how I interpreted that problem. If there is an issue with this answer, feel free to let me know.
