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Ok so here is the situation you are on a disc rotating with the same angular velocity at the center so you are in a rotating frame of reference. A block is placed.

Case 1:

The disc is frictionless. Here you would see ONLY the Coriolis force act.

Case 2:

The disc has friction and ONLY the centrifugal force acts.

So my question is when do we include centrifugal force and when do we include Coriolis force and when do both act together?

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It seems like you are under the impression that centrifugal and Coriolis forces on an object need to come from somewhere, such as from friction with the ground. They don’t. In a rotating frame of reference, they are both always there, like gravity. One or the other may be zero in special cases—if the object is on the axis of rotation, centrifugal force vanishes and if the velocity of the object is zero or parallel to the axis of rotation the Coriolis force vanishes. But conceptually they are both always present.

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If you are writing equations of motion relative to a rotating frame of reference then you always need to include three terms which are called fictitious forces - centrifugal force, Coriolis force and Euler force.

In your examples the Euler force will be zero if the angular velocity of the rotating frame of reference is constant - but it is still conceptually present.

In your second example the Coriolis force will also be zero if the block is stationary relative to the rotating frame of reference. But once again it is still conceptually present.

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