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Consider a ball placed at distance $r$ from an origin point $O$ on a horizontal plane and remains stationary.

  1. When the ball is viewed from a coordinate system which is rotating anticlockwise about $O$ with an angular velocity $\Omega$ , what is the apparent motion of the ball?
  2. What are the forces viewed from the non-rotating coordinate system?
  3. What are the apparent forces viewed in the rotating coordinate system?

From what I understand.

Let r be the position vector between origin $O$ and the ball, and r' be the position vector between the ball and the origin of the rotating frame, $O'$

  1. Since the ball itself is in the non-rotating frame and remains stationary, I am tempted to say no motion. However, considering the change in position vector r' between the ball to the rotating frame, so is the apparent motion moving in a curved path? I am having trouble to figure out who exactly observes this change in position vector. Perhaps, since the rotating frame itself is moving, it should not be observing any form of motion?
  2. There are no motions in the non-rotating frame. Thus, there should be no forces here.
  3. In general, one observes Coriolis force and centrifugal forces in a rotating frame of refence. So both forces.
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  1. The vector as an abstract object which points from the origin to the ball is independent of the coordinate system and remains constant in time. However, the coordinates of the vector do depend on the coordinate system and thus are not constant if the basis vectors are not constant.

  2. Exactly!

  3. Nope, you have the centrifugal force only, no Coriolis force. You would get a Coriolis force, if the ball had a velocity in the rest frame though.

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