Question

A uniform thin rod of length $L$ is hinged about one of its ends and is free to rotate about the hinge without friction. Neglect the effect of gravity. A force $F$ is applied at a distance $x$ from the hinge on the rod such that force is always perpendicular to the rod. Find the normal reaction at the hinge as a function of '$x$', at the initial instant when the angular velocity of the rod is zero.

Answer 1

FBD of the hinge-

The normal reaction at hinge $A$ has components $Ax$ & $Ay$.

satisfy equilibrium condition in horizontal and vertical directions-

$\sum Fx=0$

$\Rightarrow Ax=0$

$\sum Fy=0$

$\Rightarrow Ay+F=0$

$\Rightarrow Ay=-F$

So, normal reaction at hinge $A$ is $=(O\hat{i}-F\hat{j})N$