Need physics help please?

2016-02-25 4:17 pm
Find the moment of inertia of a uniform rod of length L and mass M about an axis perpendicular to the rod
and passing through the end of the rod.

回答 (2)

2016-02-25 4:41 pm
✔ 最佳答案
Let's say the rod has linear mass density λ = M / L

moment of inertia I = ∫ x² dm taken over the length of the rod (from 0 to L)

An elemental slice of the rod has mass dm = λ*dx, so
I = ∫ x² * λ * dx = λ ∫ x² dx = λx³ / 3
which, evaluated from 0 to L yields
I = λL³/3
Substitute back for λ = M/L and you get
I = (M/L)L³/3 = ML²/3
which is the accepted value for the MoI of a rod about its end.
QED

Hope this helps!
2016-02-25 4:30 pm
U should be able to find this as it is a standard configuarion:
https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=moments%20of%20interia


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