The drawing shows the top view of two doors. The doors are uniform and identical

Question

The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an axis through its left edge, and door B rotates about an axis through its center. The same force is applied perpendicular to each door at its right edge, and the force remains perpendicular as the door turns. No other force affects the rotation of either door. Starting from rest, door A rotates through a certain angle in 2.80 s. How long does it take door B (also starting from rest) to rotate through the same angle?

Explanation / Answer

since the only difference is distance away from the center from which a torque is applied the equation goes as follows Torque= I alpha Torque= 1/3 m L^2 Alpha for the hinge being at an end Torque= 1/12 m L^2 Alpha for the rotation being around the center of the door. Since everything is the same other then the coefficient in front just compare those. 1/3 to 1/12 is 4x the time it takes the door rotating about the hinge will take 4x the time it takes for the door rotating about the center.

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