Two doors are shown from the top view. The doors are uniform and identical. Door

Question

Two doors are shown from the top view. 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 F 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 3 seconds. How long does it take door B (also starting at rest) to rotate through the same angle?

Explanation / Answer

for Door A.

let length of the door is 'r'

torque about the axis = rXF = rF

and this torque = I*?

I = moment of inertia of the door about the axis of rotation.

?= angular acceleration.

I about end = (1/3)m*(r/2)2+m(r/2)2) = mr2/3

therefore,?1= rF/I = rF/(mr2/3) = 3F/(mr)

therefore,? at t= 4seconds and initial angular velocity =0

hence,? = (1/2)*?1*4 =(1/2)*(3F/(mr))*4 = 18.480769*F/(mr)

for the Door B,

I2= m(r/2)2/3 = mr2/12

torque = F*r/2 = rF/2

?2= (Fr/2)/I2= 6F/(mr)

and initial angular velocity = 0

therefore,? = (1/2)*(?2)*t2=(1/2)*(6F/(mr))*t2=3F*t2/(mr)

for the rotation of the same angle of Doors,

18.480769*F/(mr) =3F*t2/(mr)

3t2=18.480769

therefore, t =2.481986383978851seconds

will take Door B to the same angle as by Door A

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