Rolling pendulum angular acceleration

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YaniHozya
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Homework Statement
My lecturer is absent and hasn't been replying to my emails, and im unable to find much online about pendulums on trolleys so i would much appreciate any advice or help on how to do this question.
Relevant Equations
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Text of Question 3 on a physics exam: a nonuniform beam pin-supported at O on a trolley, with the angular acceleration equation theta-double-dot = (a_f d cos theta - g d sin theta) / (k_G^2 + d^2).
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  • Two-panel diagram of a rigid rod pivoted at point O on a wheeled cart. Panel (i) shows the rod hanging vertically, with distance d from O to centre of mass G and red axes a1, a2, a3 labelled A. Panel (ii) shows the cart accelerating right with acceleration a_f, the rod tilted by angle theta, and blue axes b1, b2, b3 labelled B at the rod.
    Screenshot_20210412-145556_Blackboard.jpg
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Welcome, YaniHozya!
What are those methods taught in the module that the question mentions?
Please, show us any work that you have done so far, or ask about things that you still don't understand.