Procedure:
1. Half-fill the mug with water. Carefully pour some vegetable oil into the mug so that it forms a thin layer on the surface of the water. Place a couple of drops of food colouring onto the oil.
2. Hold the rim of the mug from above. With a quick twist of your wrist turn the mug a quarter turn. What happens to the drops of food colouring?
You should see that the mug moves, but the drops of food colouring stay in the same place. This is inertia in action. The mug starts to move because you exerted a force on it. But you did not exert much of a force on the liquids in the mug because the friction between the liquids and the mug is low. The mug slides past the liquids which stay where they are. The inertia of the liquids makes them stay put.