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A rotating door is made from four rectangular sections, as indicated in the drawing. The mass of each section is 85 kg. A person pushes on the outer edge of one section with a force of F = 68 N that is directed perpendicular to the section. Determine the magnitude of the door's angular acceleration.
(r=1.2m of each door)
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For one section the moment of inertia about the axis of rotation is
I0 = 1/3*m*h**2

where: m = mass of section, h = distance to outer edge

There are 4 sections so the combined inertia is
I= 4*I0 = 4/3*m*h**2

The Torque (M) applied to the door is
M = F*h

Then
M = I0*?
? = M/I0 = (F*h)/(4/3*m*h**2)
? = 3*F/(4*m*h)

We know F = 68 N and m = 85 kg, h=1.2m
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