- #1
John Darvish
- 2
- 1
Homework Statement
I'm trying to figure out the mass moments of inertia for a hexagonal prism, with the z-axis being longitudinal. I'm trying to recall my calc 3 from 2 years ago and am failing miserably.
I know the height of the prism is h. Each hexagonal side is length a. The prism has constant density ρ. I can easily find the area and volume via relationships with equilateral triangles.
With the above dimensions and constants
ρ = m/V
m = ρ*V = 3*√3 /2 *ρ*a2*h
I initially tried to find the 3 moments of inertia just using a combination of 6 equilateral triangles. My second attempt divided up the hexagon into rectangles and then the remaining triangles. I didn't get the results I had seen via internet searches, though some of the internet searches had different results for the moments of inertia so they may have been in error.
I'm not exactly sure what I am doing right or wrong. I think my errors are in defining the dx, dy, and dz differentials when I am trying to relate dm from the general inertia formula.
∫r2 dm
I'd appreciate any help you can provide.
Thanks
John
I'm trying to figure out the mass moments of inertia for a hexagonal prism, with the z-axis being longitudinal. I'm trying to recall my calc 3 from 2 years ago and am failing miserably.
I know the height of the prism is h. Each hexagonal side is length a. The prism has constant density ρ. I can easily find the area and volume via relationships with equilateral triangles.
With the above dimensions and constants
ρ = m/V
m = ρ*V = 3*√3 /2 *ρ*a2*h
I initially tried to find the 3 moments of inertia just using a combination of 6 equilateral triangles. My second attempt divided up the hexagon into rectangles and then the remaining triangles. I didn't get the results I had seen via internet searches, though some of the internet searches had different results for the moments of inertia so they may have been in error.
I'm not exactly sure what I am doing right or wrong. I think my errors are in defining the dx, dy, and dz differentials when I am trying to relate dm from the general inertia formula.
∫r2 dm
I'd appreciate any help you can provide.
Thanks
John