A rotating door is made from four rectangular sections, asindicated in the drawi

Question

A rotating door is made from four rectangular sections, asindicated in the drawing. The mass of each section is 94 kg. A person pushes on the outer edge of onesection with a force of F = 55 N that is directed perpendicular to thesection. Determine the magnitude of the door's angularacceleration.
1 rad/s2 door is 1.2 meters wide from the center of the rotatingdoor A rotating door is made from four rectangular sections, asindicated in the drawing. The mass of each section is 94 kg. A person pushes on the outer edge of onesection with a force of F = 55 N that is directed perpendicular to thesection. Determine the magnitude of the door's angularacceleration.
1 rad/s2 door is 1.2 meters wide from the center of the rotatingdoor

Explanation / Answer

The moment of inertia of one panel is    I = (1/3) M R2 = (1/3) * 94 * ( 1.2m ) 2 = 45.12 kg.m/s2   So the total moment of inertia is    fourtimes this. Andthe torque is     force x R  or     torque = 55 N* (1.2m) finally...    torque is also defines as    = total moment of inertia (I) *   ang acc ( )    so F*R = I*    therefore = F*R/ I = (55) (1.2m) / 4*45.12 = 0.3657rad/s2

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