# Balancing & Centrifugal Force

Hi,
I've read about the balancing of rotating masses. In the context every author(even J.E.Shigley in his book Theory of machines & mechanisms) mentions that a rigid body while rotating, it experiences a "Centrifugal Force" .
Now we know that centrifugal force is a pseudo force when we analyze the motion of the body when our co-ordinate system is attached to the body.
In other case when we analyze the motion of the body when our co-ordinate system is attached to earth (inertial reference frame) there wouldn't be any centrifugal force which would then be unbalanced. So, whether the body is balanced or not depends on our selection of reference frame. I don't think that a centrifugal force is the cause of unbalance though the magnitude of unbalanced force equals/resembles that of a centrifugal force.
So,which is the force then responsible for imbalance? Detailed analysis would be appreciated.
Thanks in Advance.

## Answers and Replies

The centrifugal force which appears in a non-inertial reference frame usually ends up being explained away in an inertial reference frame.

If you analyze a system from non-inertial frame, such as taking an object in a spinning room and working from the reference of the room, the object will appear to move toward the outside of the room and stick to the wall. Applying the inertial laws of motion to this frame the only way to account for this is to add a force to move the object. This would be a centrifugal force.

If you take the same scenario from an inertial reference frame, using the laws of motion you find that this "centrifugal force" is actually just the objects inertia resisting the spinning of the room, coupled with normal forces.

My question is:
we know that centrifugal force is a pseudo force when we analyze the motion of the body when our co-ordinate system is attached to the body.
In other case when we analyze the motion of the body when our co-ordinate system is attached to earth (inertial reference frame) there wouldn't be any centrifugal force which would then be unbalanced. So, whether the body is balanced or not depends on our selection of reference frame.
This is contradictory somewhere. So what force is responsible for unbalance? Detailed derivation of force will be of great help.

K^2
Science Advisor
In inertial frame, or something sufficiently close, like Earth frame, the motion of a rigid body, such as the centrifuge, can be decomposed into translational motion of center of mass, and rotation around center of mass. The former follows the Newton's Second Law. If the body is forced to rotate around a point that does not coincide with center of mass, center of mass is accelerating. That means there is a force applied to the centrifuge, and by Newton's Third to the base of the centrifuge. Since the acceleration of mass is always towards center of rotation, the force applied to the base is also rotating with the same angular frequency. There is your unbalance force in inertial frame.

Does that help?

Ya surely. Thanks.