Why Is It Harder to Rotate A Rod with a Mass in the Center?

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Homework Help Overview

The discussion revolves around the difficulty of rotating two different configurations of a rod: one with a mass at the center and another with masses at the ends. The original poster expresses confusion regarding their professor's assertion that the rod with the mass in the center is harder to rotate, especially given the assumption that the total mass is equal in both cases.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between moment of inertia and rotational difficulty, questioning whether the configuration with the mass in the center indeed requires more work to achieve the same angular velocity. Some participants suggest that the original poster may have misunderstood the professor's explanation.

Discussion Status

The discussion is ongoing, with participants providing differing perspectives on the moment of inertia and its implications for rotational motion. There is a recognition of potential misunderstandings regarding the professor's statement, and some participants are considering seeking further clarification.

Contextual Notes

Assumptions about the axis of rotation and the distribution of mass are central to the discussion, with participants noting the importance of these factors in determining the moment of inertia for each configuration.

sagebum
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Homework Statement


Which is harder to rotate?
A rod with a mass (m1) in the center, or a rod with two masses (m2)at the ends.
Assume mass m1 = 2*m2, so the total masses of rod+masses are equal.
I am rotating the masses at the center.

My professor said that the one with the mass in the center is harder to rotate, but I don't understand how he explained it. I actually thought the one with the mass in the center was easier to rotate.

Can someone explain why the one with the mass in the center is harder to rotate?
Is it because if we were to rotate each to the same angular velocity, it would take more work to get the first rod to that angular velocity?

Relevant equations.
I think I'd use Kr = I [tex]\omega^{2}[/tex]
and if they go up to the same angular velocities, it requires more work?
It doesn't seem right, because if the I of the first rod is lower, so the Kr would be lower, so that means the work required to get it to that speed was lower?
I don't see why the one with the mass in the center is easier to rotate.
 
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assuming that you are rotating about an axis that goes thru the center then it would harder to rotate the m2 case because it has larger moment of inertia. unless i have misunderstood the setup.
torque = moment of inertia x angular acceleration
you may have mis-heard your prof.. or there are something else in the system?
 
sagebum said:

Homework Statement


Can someone explain why the one with the mass in the center is harder to rotate?
Is it because if we were to rotate each to the same angular velocity, it would take more work to get the first rod to that angular velocity?

It wouldn't take any energy to rotate the rod with m1 in the centre, because the velo of the point mass at the centre would be zero.

Perhaps you misunderstood your professor, as mjsd says?
 
Yeah, I thought what u said was the answer too, I'll have to ask my professor again, maybe i switched up what he said.

Thanks for helping
 

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