Calculate Friction Required for Rolling Without Slipping (Down a Hill) | Force

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Calculate the required coefficient of static friction required for an object to roll down a hill without slipping.
The coefficient of friction must be adequate to cause a rotational acceleration that is consistent with the translational acceleration of the wheel.
This solution works for any round shape of object so long as it has a consistent radius and a known moment of rotational inertia.
This problem comes up in introductory physics courses including AP Physics 1, AP Physics C Mechanics and appears on the JEE as well as A Level Physics Exam.