What Fraction of Initial Height Causes a Plank to Lose Wall Contact?

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The discussion revolves around determining the fraction of the initial height at which a plank loses contact with a wall as it slips down without friction. The participants analyze the forces acting on the plank, particularly the normal forces from the wall and the floor, and derive equations of motion based on energy conservation and angular dynamics. They clarify the coordinate system and the relationships between the angles and positions of the center of mass. The conversation includes attempts to solve a second-order differential equation that describes the motion of the plank, with insights on using energy methods for simplification. Ultimately, the focus is on deriving the conditions under which the plank loses contact with the wall.
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Tanya Sharma said:
One thing I need to clarify is that θ is measured from the horizontal with clockwise being the direction of increasing θ .

Does that mean direction of increasing θ has to be considered positive ?
Yes, cw would be the positive direction for θ.

Does this reflect on the direction of torque as well with clockwise torque being considered positive and ccw negative ?
Yes. I believe you set up your torque equation with the correct signs.
 

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