Question

A thin horizontal uniform rod `AB` of mass `m` and length `l` can rotate freely about a vertical axis passing through its end `A`. At a certain moment, the end `B` starts experiencing constant force `F` which is always perpendicular to the original position of the stationary rod and directed in a horizontal plane. Find the angular velocity of the rod as a function of its rotation angle `phi` counted relative to the initial position.

Answer 1

`tau_(o)=Fcosphi l=I_(0)alpha=(ml^(2))/(3)alpha`
`alpha=(3Fcosphi)/(ml)` (variable angular acceleration)
`omega(domega)/(dphi)=(3Fcosphi)/(ml)`
`int_(0)^(omega)omega domega=(3F)/(ml)int_(0)^(omega)cosphidphi`
`(omega^(2))/(2)=(3F)/(ml)sinphi implies sqrt((6fsinphi)/(ml))`