# What is the relationship between the moment of inertia and the length of a rod?

• merlos
In summary, the moment of inertia for a rod about an axis along its length is calculated by adding the moment of inertia for a rod about its center (I = (1/4)MR^2) and the moment of inertia for a rod about one end (I = (1/3)ML^2). The length of the rod does not affect the calculation, only the radius.
merlos
The moment of inertia about an axis along the length of a rod is zero, correct?

merlos said:
The moment of inertia about an axis along the length of a rod is zero, correct?
Almost. If the rod has a measurable radius, it is a cylinder.

In all the other parts ot the problem though I considered it a rod.

Here's the problem:

Find the moment of inertia about each of the following axes for a rod that is 0.280 cm in diameter and 1.70 m long, with a mass of 5.00×10−2 kg.

A. About an axis perpendicular to the rod and passing through its center.
I = (1/12)ML^2
I = .012 kgm^2

B. About an axis perpendicular to the rod passing through one end.
I = (1/3)ML^2
I = .048 kgm^2

C. About an axis along the length of the rod.

merlos said:
In all the other parts ot the problem though I considered it a rod.

Here's the problem:

Find the moment of inertia about each of the following axes for a rod that is 0.280 cm in diameter and 1.70 m long, with a mass of 5.00×10−2 kg.

A. About an axis perpendicular to the rod and passing through its center.
I = (1/12)ML^2
I = .012 kgm^2

B. About an axis perpendicular to the rod passing through one end.
I = (1/3)ML^2
I = .048 kgm^2

C. About an axis along the length of the rod.
The rod has a diameter. It has a moment of inertia about the long axis.

So, I = (1/4)MR^2 + (1/3)ML^2 ?

The length of the stick--or cylinder--parallel to the axis doesn't matter, only the radius.

## 1. What is the moment of inertia of a rod?

The moment of inertia of a rod is a measure of its resistance to rotational motion. It is a property of the rod that depends on the distribution of mass along its length and the axis of rotation.

## 2. How is the moment of inertia of a rod calculated?

The moment of inertia of a rod can be calculated using the formula I = (1/12) * m * L^2, where m is the mass of the rod and L is the length of the rod.

## 3. Why is the moment of inertia of a rod important?

The moment of inertia of a rod is important because it helps us understand how it will behave when subjected to rotational forces. It is also used in many engineering and physics calculations, such as determining the torque required to rotate the rod.

## 4. How does the shape of a rod affect its moment of inertia?

The shape of a rod can greatly affect its moment of inertia. A rod with a larger diameter will have a higher moment of inertia than a rod with a smaller diameter, even if they have the same length and mass. Additionally, a rod with a non-uniform distribution of mass will have a different moment of inertia than a rod with a uniform distribution of mass.

## 5. Can the moment of inertia of a rod be changed?

Yes, the moment of inertia of a rod can be changed by altering its mass distribution. For example, by adding weights to one end of the rod, the moment of inertia will increase. Additionally, changing the axis of rotation can also change the moment of inertia of a rod.

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