Calculating the moment of inertia for this configuration

[Demon117]

Homework Statement

I need to find the rotational kinetic energy of this system in the figure I have provided. Here the spring is rotating with the system at angular speed $\omega$. The two beads on the wire move vertically, and the third bead is held by two massless rods of equal length L.

The Attempt at a Solution

Would the moment of inertia for the the whole thing just be

$I_{1,3}=2mL^{2}$

$I_{2,3}=2mL^{2}$

$I_{total}=4mL^{2}$

Any suggestions would be helpful.

 

[SammyS]

Homework Statement

I need to find the rotational kinetic energy of this system in the figure I have provided. Here the spring is rotating with the system at angular speed $\omega$. The two beads on the wire move vertically, and the third bead is held by two massless rods of equal length L.

The Attempt at a Solution

Would the moment of inertia for the the whole thing just be

$I_{1,3}=2mL^{2}$

$I_{2,3}=2mL^{2}$

$I_{total}=4mL^{2}$

Any suggestions would be helpful.

It looks as though the system is constrained to rotate about the z-axis.

You need to find the moment of inertia about the z-axis.

 

[Demon117]

Will it depend on the angle $\alpha$?

 

[SammyS]

Will it depend on the angle $\alpha$?

Yes it will depend on α .

 

[paranormal]

I would like to clarify that the moment of inertia is a measure of an object's resistance to rotational motion and is dependent on the distribution of mass and the axis of rotation. In this case, the moment of inertia for the entire system would not simply be the sum of the moment of inertia for each individual component.

To accurately calculate the moment of inertia for this configuration, we would need to consider the contributions from each component, such as the two beads on the wire and the third bead held by the rods, as well as the spring and its rotational motion. This would involve using the parallel axis theorem and possibly integrating over the entire system to account for the distribution of mass.

Additionally, to calculate the rotational kinetic energy of the system, we would need to know the moment of inertia and the angular velocity, not just the moment of inertia. I would suggest consulting with your textbook or a reliable source for the appropriate equations and steps to calculate the moment of inertia and rotational kinetic energy for this specific system.