How can I find the inertia of a rod with a pivot point?

In summary, the inertia of a rod with a pivot point somewhere along its length can be calculated using the parallel axis theorem: I = Ic + (md^2), where Ic is the moment of inertia about the center of mass and d is the distance between the parallel axes passing through the center of mass and the pivot point. This can be proved and then applied to find the inertia of the rod. The center of mass for the rod is located at L/2 from one end and the pivot point is at 2L/3 from one end, resulting in a distance of d = L/6. Ic is equal to m*L2/12, where m is the mass of the rod and L is its length
  • #1
Blockade
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0
I have a question on finding the inertia of a rod with a pivot point somewhere along it's length.

So the inertia of a rod is IStick cm = 1/12 *m*L2
Does L2 = (2L/3)2 = 4L2/9 -> 1/12 *m*[4L2/9] or is it something like
m*L2/12 + m* (2L/3)2?

If it's the second one then may I ask why it's that?

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  • #2
Revise parallel axis theorem; I = Ic + (md^2) Ic is MI about CM and d is the distance between parallel axes passing through CM and pivot. It can be proved first and then can be used.
 
  • #3
Let'sthink said:
Revise parallel axis theorem; I = Ic + (md^2) Ic is MI about CM and d is the distance between parallel axes passing through CM and pivot. It can be proved first and then can be used.

so m*L2/12 + m* (2L/3)2
where Ic = m*L2/12
and md^2 = m* (2L/3)2when you said "MI about CM" you mean the mass around the center mass which is the entire rod? As for d is the "distance between parallel axes passing through CM and pivot" meaning the length between the end of the stick pass the center mass where it ends at the pivot?
 
  • #4
center of mass is at the mid point of rod at L/2 from one end and if pivot is at 2L/3 from one end then d = (2L/3) - (L/2) = L/6. Ic is the MI about the axis passing through the point at L/2 from one end.
 

FAQ: How can I find the inertia of a rod with a pivot point?

How do I calculate the inertia of a rod with a pivot point?

To calculate the inertia of a rod with a pivot point, you will need to know the mass of the rod, the distance between the pivot point and the center of mass of the rod, and the length of the rod. You can use the formula: I = (1/3) * m * L^2, where I is the inertia, m is the mass, and L is the length. Make sure to use the distance between the pivot point and the center of mass, rather than the entire length of the rod.

Can I use the same formula to calculate the inertia of any object?

No, the formula (I = (1/3) * m * L^2) is specifically for calculating the inertia of a rod with a pivot point. For other objects, you will need to use different formulas that take into account the shape, mass distribution, and axis of rotation of the object.

What is the importance of finding the inertia of a rod with a pivot point?

Finding the inertia of a rod with a pivot point is important in understanding how the rod will move and respond to external forces. It can also be used in engineering and design to ensure the stability and functionality of structures that involve rods with pivot points.

How can I measure the distance between the pivot point and the center of mass of the rod?

The distance between the pivot point and the center of mass can be measured using a ruler or measuring tape. Place one end of the measuring tool at the pivot point and measure the distance to the center of mass, which can typically be found at the center of the rod. You can also use a balance scale to find the center of mass by balancing the rod on a pivot point and measuring the distance from each end of the rod to the pivot point.

Can the inertia of a rod with a pivot point change?

Yes, the inertia of a rod with a pivot point can change if the mass or the distance between the pivot point and the center of mass changes. It can also change if the rod is rotated to a different angle, as the distance between the pivot point and the center of mass will be different. However, if the mass and distance remain constant, the inertia will not change.

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