A horizontally oriented uniform rod AB of mass `m=1.40kg` and length `l_0=100cm` rotates freely about a stationary vertical axis `OO^'` passing through its end A. The point A is located at the middle of the axis `OO^'` whose length is equal to `l=55cm`. At what angular velocity of the rod the horizontal component of the force acting on the lower end of the axis `OO^'` is equal to zero? What is in this case the horizontal component of the force acting on the upper end of the axis?

Explanation

The total centrifugal force can be calculated by,
`underset(0)overset(l_0)int(m)/(l_0)omega^2xdx=1/2ml_0omega^2`
Then for equilibrium,
`(T_2-T_1)l/2=mgl_0/2`
and, `T_2+T_1=1/2ml_0omega^2`
Thus `T_1` vanishes, when
`omega^2=(2g)/(l)`, `omega=sqrt((2g)/(l))=6rad//s`
Then `T_2="mg" (l_0)/(l)=25N`