What is the force at the axis of a rotating rod

[Karol]

Homework Statement

A force is rotating the rod of mass m and length l round it's endpoint, according to drawing.
The force rotates either, so as to simplify the problem.
What force, apart from the one opposed to the centrifugal force, acts at the bearing?

Homework Equations

$$M=I\alpha$$

The Attempt at a Solution

I calculate the moment M and moment of inertia I about the rotation point A, then I find the angular acceleration $\alpha$:

$$F\frac{l}{2}=\frac{ml^2}{3}\cdot\alpha$$

$$\Rightarrow\alpha=\frac{3F}{2ml}$$

I assume I can take any point, calculate the moment of inertia round it, and using, again, equation $M=I\alpha$ and knowing that the angular accelaration $\alpha$ should be the same, I calculate the moment round that point:
I choose point B:

$$M=\frac{ml^2}{12}\cdot\frac{3F}{2ml}=\frac{Fl}{8}$$
$$\Rightarrow F_{B}=\frac{F}{4}$$

 

[tiny-tim]

Hi Karol!

(have an alpha: α )

I assume I can take any point, calculate the moment of inertia round it, and using, again, equation $M=I\alpha$ and knowing that the angular accelaration $\alpha$ should be the same, I calculate the moment round that point:
I choose point B …

Yes, that's fine, and F/4 is correct (though you needn't actually have found α … you could have used a formula combining the two equations, with no α).

(Alternatively, you could have used sum of forces = mass times acceleration of centre of mass instead of one of the moment of inertia equations. )

 

[Karol]

Thanks again, fish...