A rod of length L has a mass density given by λ = λo(1 – x/L). What is the rod’s rotational inertia measured about the end where x = 0? Write your answer in terms of its total m…

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asked Apr 10, 2020 26.6k views

1 Answer

Ashox · Answer 1 · 2020-04-15T19:48:59+0000

Answer:

$I = (\lambda_o L^3)/(12)$

Step-by-step explanation:

Rotational inertia of the rod about its one end is given as

$I = \int dm x^2$

here we know that

$dm = \lambda dx$

so we will have

$I = \int (\lambda dx) x^2$

$I = \int \lambda_o(1 - x/L) x^2 dx$

so we have

$I = \lambda_o((L^3)/(3) - (L^3)/(4))$

$I = (\lambda_o L^3)/(12)$