A rod is nailed (flexibly) to a wall at one end. The other end is held up from letting the rod swing by a thread connected to the ceiling. The rod has mass M and length l. The moment of inertia is (Ml^2)/3. Determine the magnitude and direction of the force exerted on the rod by the axis. Express in terms of M, l, and g.
Here is my thinking...
Torque provided by the nail in the wall is opposite of the torque provided by the thread. Torque, T=lF=I(alpha). I=(Ml^2)/3. Alpha=a/l. So F=ma/3. But that is WRONG. Why?????
The nail does not provide torque. The rod is supposedly free to swing about the nail, but it kept from swinging by the thread.
If the rod is not swinging, the moment of inertia does not affect the force balance. Set the total torque about the nail equal to zero. Regardless of the angle A >0 that the rod is tilted, the thread force at the end must be half the weight force applied at the center of mass. A torque balance tells you that.
Therefore the string tension is W/2. Now perform a vertical force static balance to determine the vertical force applied by the nail.