Solve the Problem of Rotating a Strangely-Shaped Slab

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The discussion revolves around calculating the angle of rotation for a uniquely shaped slab with a mass of 3.0 kg, subjected to an 8.0 Newton force. A participant suggested using the r^2 dm method, but another contributor clarified that the area of the object must be considered instead. The correct approach involves understanding the slab's geometry and applying relevant physics principles to find the angle after 20 seconds. Participants are seeking guidance on the proper formula to use for this calculation. The conversation emphasizes the importance of accurately interpreting the problem's requirements.
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The problem is:
A thin slab of material of uniform density with a total mass 3.0 kg is cut in a strange shape: It is bounded by the curves y=4-x^2 and x=0. Initially it is lying in the xy plane. It is free to rotate about the y axi. A force of 8.0 Newtons is constantly applied perpendicular to the slab at the outer bottom corner. What angle (In radians) has it rotated through after 20 seconds?

A helper on this forum told me to do r^2 dm. However my professor say that this is incorrect and that I need to use the are of the object to answer the problem.

If anybody can help me solve this problem it would be very much appreciated!
 
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