Short Question about Torque on a Ladder Hinge

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To find the torque about the hinge of a ladder due to its own weight, the relevant equation is τ = r x F, where r is the perpendicular distance from the hinge to the line of action of the force. The torque can be calculated using the formula τ = (M_ladder / 2) * g * (L/2) * sin(α), where M_ladder is the mass of the ladder, g is the acceleration due to gravity, and α is the angle with the vertical. The distance r should be the horizontal component of the ladder's length, specifically L * sin(α) / 2, as this represents the center of mass of the ladder. The angle α is defined as the angle the ladder makes with the vertical. This approach correctly accounts for the torque generated by the ladder's weight about the hinge.
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Homework Statement


So this is a small part of a much larger problem that I'm working on that I don't want to post here. Basically, I want to find the contribution to the torque about the hinge of a ladder BY the mass of the ladder itself. A ladder is propped open at an angle α. What is the torque about the hinge of the top of the ladder of length L by the ladder itself?

Homework Equations


τ = r x F

The Attempt at a Solution


Will the torque from one side of the ladder I'm ignoring the other side of the ladder for now). be M_ladder / 2 * g * L/2 sinα ? I'm basically wondering what to put for r, the perpindicular distance from the force applied to the point of torque. Should it just be the center of that side of the ladder? In that case, should it be Lsinα /2?
 
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Are alpha the angle one leg encloses with the vertical, and M the total mass of the ladder? In that case, the expression for the torque due to the weight is correct.
 

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