Show that the moment of inertia of a uniform rod of length L and mass M about an axis perpendicular to the
rod and passing through its center of mass is
1/12*ML^2
Physics help please!!?
2016-02-25 4:37 pm
回答 (1)
2016-02-25 6:16 pm
✔ 最佳答案
Let's say the rod has uniform mass density λ = M/Lwhere M is the mass and L the length.
MoI I = ∫ x² dm = ∫ x² * λ dx = λ ∫ x² dx →evaluated from -L/2 to L/2
I = λ * x³/3 |[-L/2,L/2] = λ/3 * (L³/8 - -L³/8) = λ/3 * L³/4
When we substitute λ = M/L, we get
I = (M / 3L) * L³/4 = ML² / 12 ◄
QED
Hope this helps!
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