# Calculate Moment of Inertia of Rods | Solution Included

• supercali
In summary, the moment of inertia for two rods with mass m and length L about their center of mass is given by \frac{L^2m}{12}*2+\frac{L^2m}{8}*2. The center of mass is located at \frac{L}{4}\hat{x}-\frac{L}{4}\hat{y} and the distance from each rod to this center of mass must be taken into account using the parallel axis theorem. In the case of a square of rods, there would be a factor of 4 involved due to the different distances from each rod to the center of mass.
supercali
[SOLVED] moment of inertia

## Homework Statement

what is the moment of interia of these 2 rods (picture attached) about their center of mass
each rod mass is m with length L

## Homework Equations

one rod i know is $$\frac{L^2m}{12}$$

## The Attempt at a Solution

#### Attachments

• Clip_2.jpg
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First things first: Find the center of mass.

good question

i thought the answer is $$\frac{L^2m}{12}*2+\frac{L^2m}{4}*2$$
obviously it isnt

i think center of mass is at $$\frac{L}{4}\hat{x}-\frac{L}{4}\hat{y}$$

Last edited:
supercali said:
i think center of mass is at $$\frac{L}{4}\hat{x}-\frac{L}{4}\hat{y}$$
Good--it's right in the middle between the two rod centers. So what's the distance from the center of each rod to that center of mass? To find the rotational inertia of the rods about that center of mass, use the parallel axis theorem.

yeah i got it it is $$\frac{L^2m}{12}*2+\frac{L^2m}{8}*2$$ and one more thing if it was a square or rods i would have to multiply by 4?

supercali said:
yeah i got it it is $$\frac{L^2m}{12}*2+\frac{L^2m}{8}*2$$
Good.
and one more thing if it was a square or rods i would have to multiply by 4?
If it were a square of rods, the distance from each rod to the center of mass would be different. (But there would be a factor of 4 involved.)

## 1. What is Moment of Inertia?

Moment of Inertia is a measure of an object's resistance to changes in its rotational motion. It is the sum of the products of each particle's mass and its square distance from the axis of rotation.

## 2. How do you calculate Moment of Inertia for a rod?

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. What units are used for Moment of Inertia?

Moment of Inertia is typically measured in units of kilogram meter squared (kgm^2).

## 4. Can Moment of Inertia be negative?

No, Moment of Inertia cannot be negative as it is a physical property that represents an object's resistance to rotational motion.

## 5. 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 radius or thicker diameter will have a greater Moment of Inertia compared to a rod with a smaller radius, even if their masses are the same. The distribution of mass along the axis of rotation also affects the Moment of Inertia.

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