- #1

Soren4

- 128

- 2

## Homework Statement

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Consider a barbell with two equal masses [itex]m[/itex] that rotates around a vertical axis [itex]z[/itex] not passing through its center with angular velocity [itex]\vec{\omega}[/itex]. The barbell is forced to stay in this position by an appropriate support.

Identify the forces exerting torques on the system and explain what are their effects.

## Homework Equations

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Taking a generic point [itex]P[/itex] on the [itex]z[/itex] axis as pivot point to calculate momenta, the total angular momentum [itex]\vec{L}=\vec{L_1}+\vec{L_2}[/itex] is not parallel to the rotation axis [itex]z[/itex], thus [itex]\vec{L}[/itex] follows a precession motion and, from the theorem of angular momentum, there must be a torque [itex]\vec{\tau}[/itex] on the system, exterted by external forces: [itex]\vec{\tau}=\frac{d \vec{L}}{dt}\neq 0[/itex].

## The Attempt at a Solution

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The external forces that have non zero torque are weight (because [itex]\vec{r_1} \neq \vec{r_2} [/itex]) and the reaction of the support. But, since the barbell is forced in this position during the motion, the torque of these two forces should add up to zero ([itex] \vec{\tau}=0[/itex]). On the other hand this is not possible, since [itex]\vec{L}[/itex] is changing over time. How can that be?