Finding Center of Mass of Two Rods

In summary: Assuming the rods are uniform and laid end to end, the center of mass of the system will be within the heavier rod. The exact position will depend on the dimensions of the heavier rod.
  • #1
schaafde
16
0
I am currently trying to find the center of mass of two rods. One rod is 20 2/3 oz and is 17 inches long with a diameter of 3. The other rod is 10 1/3 oz and 17 inches long with a diameter of 1 1/2 The bigger rod is touching the smaller one if they were both standing up. It looks almost like a bottle. Would I just take the center of mass of each rod and average them together with the bigger rod accounting for more or is that too simple?
 
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  • #2
schaafde said:
Would I just take the center of mass of each rod and average them together with the bigger rod accounting for more or is that too simple?
That's all there is to it.
 
  • #3
Would that be the same for finding the moment of inertia for that system? just find the moment of inertia for each individual rod and average them together?
 
  • #4
schaafde said:
Would that be the same for finding the moment of inertia for that system? just find the moment of inertia for each individual rod and average them together?
No, you wouldn't average them. You'd add them. (Make sure you have the moment of inertia of each about the same axis.)
 
  • #5
So i calculated the center of mass to be 2/3 of the way up the "object" which would make it in the bigger rod? Would I be correct in assuming that? I am going off the fact that a uniform rod would have its center of mass directly in the middle.
 
  • #6
schaafde said:
So i calculated the center of mass to be 2/3 of the way up the "object" which would make it in the bigger rod? Would I be correct in assuming that?
Did you assume it or calculate it? Yes, assuming the rods are uniform and laid end to end, the center of mass of the system will be within the heavier rod. Calculate the exact position.
I am going off the fact that a uniform rod would have its center of mass directly in the middle.
Good.
 

1. How do you calculate the center of mass of two rods?

The center of mass of two rods can be calculated by finding the individual centers of mass for each rod and then using the weighted average formula to determine the overall center of mass. This involves taking into account the masses and distances of each rod from a reference point.

2. What is the importance of finding the center of mass of two rods?

Finding the center of mass of two rods is important in understanding the stability and balance of a system. It can also be used to determine the force exerted on the system by an external force, as well as the overall motion and rotation of the system.

3. Can the center of mass of two rods be outside of the physical structure?

Yes, the center of mass of two rods can be outside of the physical structure. This can occur if the distribution of mass is uneven or if one of the rods is significantly longer than the other. In such cases, the center of mass may be located in empty space.

4. How does the center of mass change if one of the rods is moved?

If one of the rods is moved, the center of mass will also shift. The new center of mass will depend on the mass and distance of the moved rod, as well as the position of the other rod. The overall center of mass may also shift if the mass of the rods is not evenly distributed.

5. Is there a limit to the number of rods that can be used to find the center of mass?

No, there is no limit to the number of rods that can be used. The same principles of calculating the center of mass of two rods can be applied to any number of rods. However, as the number of rods increases, the calculations become more complex and may require advanced mathematical methods.

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