Calculate Moment of Inertia of Rods | Solution Included

[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

 

[Doc Al]

First things first: Find the center of mass.

 

[supercali]

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}

 

[Doc Al]

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.

 

[supercali]

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?

 

[Doc Al]

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.)