Here is another more general case: You can drag the Force arrow to change it's direction.

1. Choose the center of the disk as origin.

Assume the friction force is f, The x, y component of the external force F is Fx, Fy

Then from Newton's law:

The Net torque is

Assume the disk motion satisfy "Rolling Without Slipping" condition: i.e.

So

We will get

is the new "Moment of inertia" if we move the origin to the point disk in contact with the surface.

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