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

  • Thread starter sagebum
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In summary, the one with the mass in the center is harder to rotate because it takes more work to get it to the same angular velocity as the rod with m2 at the ends.
  • #1
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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  • #2
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?
 
  • #3
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?
 
  • #4
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
 

1. Why does adding a mass to the center of a rod make it harder to rotate?

When a mass is added to the center of a rod, it increases the moment of inertia of the system. This means that there is more resistance to changes in the rotational motion of the rod. Therefore, it becomes harder to rotate the rod with a mass in the center.

2. How does the distribution of mass affect the difficulty of rotating a rod?

The distribution of mass along the length of a rod plays a significant role in the rotation of the rod. When the mass is concentrated at the center, it increases the moment of inertia and makes it harder to rotate. On the other hand, if the mass is distributed evenly along the length of the rod, it decreases the moment of inertia and makes it easier to rotate.

3. Is there a specific formula to determine the difficulty of rotating a rod with a mass in the center?

Yes, the moment of inertia of a rod with a mass in the center can be calculated using the formula I = MR^2, where M is the mass of the rod and R is the distance from the center of mass to the axis of rotation. The larger the moment of inertia, the harder it is to rotate the rod.

4. Can the shape of the rod affect how difficult it is to rotate it with a mass in the center?

Yes, the shape of the rod also plays a role in the difficulty of rotation. A rod with a larger diameter will have a larger moment of inertia and will be harder to rotate compared to a rod with a smaller diameter. Additionally, the distribution of mass along the length of the rod can also affect the difficulty of rotation.

5. How can adding a mass to the center of a rod affect other physical properties?

Adding a mass to the center of a rod not only affects its rotational motion but also other physical properties such as its center of mass and its stability. The added mass can shift the center of mass, making the rod more difficult to balance. It can also affect the stability of the rod, making it more prone to tipping over.

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