So, I'm trying to study phase shift in an unbalanced rotating system (where "phase shift" means the resulting response of orbital motion lags behind in time/position relative to the force that's causing it)
I know that conservation of angular momentum applies ideally in a closed system. Would it apply in any form in a system like the following? ....
![]()
Take a highly unbalanced disk (like in a Jeffcott rotor, for anyone familiar), connected by a flexible shaft constrained at both ends. Assume that a constant steady input torque is applied to the shaft/disk at its radial center, creating a constant increase in angular velocity. With added speed, the shaft will increasingly bend and the disk will deflect and orbit in some enlarging translational path, while still spinning synchronously. The torque still remains applied to the radial center of the disk. Assume the shaft and supports are isotropic, and create a circular orbit.
Since the same input torque is causing both the spin and the translation orbit, causing the spin directly and indirectly causing the orbit (via reactive centrifugal force), is it possible to "normalize" the torque input and consider the two motions in a comparative manner as if it were a closed system? The same object with the same single input torque is in two rotational motions, but one rotation has a steadily increasing radius while the other rotation has no change in radius.
In this situation, would some form of conservation of angular momentum cause the angular velocity of the object's orbit (with growing radius) to increase more slowly relative to the angular velocity of the object's spin (with a constant zero-radius)?
*****
It's well known that this relative slowing (phase shift) happens in practice, but it is classically attributed only to external damping in the supports/bearings and/or to internal damping in the shaft material (both cases are typically modeled as a linear mass-spring-damper system). But in this example, there is no motion in the bearings (like in fixed ball bearings for instance), and since the shaft is synchronously orbiting in a circular path, with the same side always facing outward, there is no oscillation in the material of the shaft. Since damping requires motion/velocity to do anything, damping wouldn't have a source here it seems.
I know that conservation of angular momentum applies ideally in a closed system. Would it apply in any form in a system like the following? ....
Take a highly unbalanced disk (like in a Jeffcott rotor, for anyone familiar), connected by a flexible shaft constrained at both ends. Assume that a constant steady input torque is applied to the shaft/disk at its radial center, creating a constant increase in angular velocity. With added speed, the shaft will increasingly bend and the disk will deflect and orbit in some enlarging translational path, while still spinning synchronously. The torque still remains applied to the radial center of the disk. Assume the shaft and supports are isotropic, and create a circular orbit.
Since the same input torque is causing both the spin and the translation orbit, causing the spin directly and indirectly causing the orbit (via reactive centrifugal force), is it possible to "normalize" the torque input and consider the two motions in a comparative manner as if it were a closed system? The same object with the same single input torque is in two rotational motions, but one rotation has a steadily increasing radius while the other rotation has no change in radius.
In this situation, would some form of conservation of angular momentum cause the angular velocity of the object's orbit (with growing radius) to increase more slowly relative to the angular velocity of the object's spin (with a constant zero-radius)?
*****
It's well known that this relative slowing (phase shift) happens in practice, but it is classically attributed only to external damping in the supports/bearings and/or to internal damping in the shaft material (both cases are typically modeled as a linear mass-spring-damper system). But in this example, there is no motion in the bearings (like in fixed ball bearings for instance), and since the shaft is synchronously orbiting in a circular path, with the same side always facing outward, there is no oscillation in the material of the shaft. Since damping requires motion/velocity to do anything, damping wouldn't have a source here it seems.