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 2.53 s. How long does it take door B (also starting from rest) to rotate through the same an

Explanation / Answer

Door A:

say L = disatance between force applied and axis

T = torque

T= F * L

Moment of Inertia(M1) = 1/3 * m * L^2

Door B:

Torque = F * L/2

moment of inertia*(M2) = 1/12 * m * L^2

this can be wrtten as Moment of interia = 1/4(M1)

so for same angel time taken in 1/4 of the time taken for Door A

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