Solution - Minimum Friction

First, define .

Then, draw all forces that works on the rod. The total force and torque on the rod must be zero, because it is in equilibrium.

For x-component,

For y-component,

And for torque, we can take an arbitrary point on the rod because it is in equilibrium. In this case, we take the contact point to the floor.

Solving these three equations, and we get the relation between and ,

Because and may have different values, the coefficient of friction of wall and floor must be the greatest value between these two values, and , to keep the value of both not higher than the coefficient of friction.

Then draw a graph with as x-axis and as y-axis (can be or ).


From the graph, we can conclude that it reach its minimum value when .

And the equation (4) will become

Solve for ,

That's my solution.
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