A rotating door is made from four rectangular glass panes, as shown in the drawing. The mass of each pane is 88 kg. A person pushes on the outer edge of one pane with a force of F = 53 N that is directed perpendicular to the pane. Determine the magnitude of the door's angular acceleration.

In the drawing the radius is 1.2m and F is counterclockwise.

Net external torque=moment of Inertia X Angular acceleration

Moment of Inertia = sum of mass X r^2
= (88kg X 4)(1.2m^2)
=506.88

I transpose the above formula making angular acceleration the subject of the equation.

Angular acceleration= sum of external torque / Moment of inertia

angular acceleration= 63.6 / 506.88
=0.12547

This answer is incorrect please tell me where I went wrong.

The moment of inertia depends upon where the glass panes are placed, which your question does not explain. it is unfortunate that this web site cannot handle figures. In any case, the moment of inertia is not just the sum of masses of the panes multipied by some R^2. You have to use the parallel axis theorem. See
http://hyperphysics.phy-astr.gsu.edu/hbase/parax.html

I apologize for the confusion. You are correct that the moment of inertia of the rotating door depends on the placement of the glass panes. In this case, since the question does not provide specific information about the placement, we cannot accurately determine the moment of inertia without that information. The parallel axis theorem is indeed the correct method to calculate the moment of inertia for a system with rotating objects that are not necessarily rotating around their center of mass.

To use the parallel axis theorem, you would need the individual distances of each glass pane from the axis of rotation. Once you have those distances, you can calculate the moment of inertia for each pane using the formula:

I = m * (r^2)

where m is the mass of the pane and r is the distance of the pane from the rotation axis. Then, you can sum up the individual moments of inertia to get the total moment of inertia for the door.

Once you have the correct moment of inertia, you can proceed to find the angular acceleration using the formula:

angular acceleration = sum of external torque / moment of inertia

Considering the information provided in the question, it seems we would need more details to accurately solve this problem.