The easiest derivation of rod's moment of inertia?

• Glyper
In summary, the formula for a rod's moment of inertia is I = ml2/12, which can be derived by dividing the rod into two parts and integrating from 0 to l/2. Another method is to consider a small infinitesimal piece at a distance 'dr' from the center of mass of the rod and using the fact that mass = mass per unit length * distance. This results in the formula I = ∫ r2 dm.
Glyper

Homework Statement

Derive the formula for rod's moment of inertia: I = ml2/12

I = ml2/12

The Attempt at a Solution

The only one derivation I know of is dividing the rod into two parts and then integrating from 0 to l/2. However' I'd love to know if there's some easier (or more "natural"?) way to do it? Or, if not, maybe you know some website where it's explained as if I were five so that I can get the grasp of it? Because looking at bare integrals, I don't quite know what I'm calculating.

I think the easiest way would be to just do the integral.

I= ∫ r2 dm

If you consider a small infinitesimal piece at a distance 'dr' from the center of mass of the rod, the mass of this piece will be dm.

Then you just use the fact that mass = mass per unit length * distance i.e. dm = M/L * dr

I see. Thanks :)

1. What is the formula for calculating a rod's moment of inertia?

The formula for calculating a rod's moment of inertia is I = (1/12) * m * L^2, where I is the moment of inertia, m is the mass of the rod, and L is the length of the rod.

2. Is this formula specific to a certain type of rod?

No, this formula can be applied to any rod as long as the rod has a uniform mass distribution.

3. Can this formula be used to calculate the moment of inertia for objects other than rods?

No, this formula is specifically designed for calculating the moment of inertia for rods. Other objects may have different formulas for calculating their moment of inertia.

4. What are the units for moment of inertia?

The units for moment of inertia are kg*m^2.

5. How does the length of the rod affect its moment of inertia?

The longer the rod, the larger the moment of inertia will be. This is because the moment of inertia is directly proportional to the square of the length of the rod, as seen in the formula I = (1/12) * m * L^2.

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