A thin rod of length has a linear mass density given by

PHYSICS · Single correct · AP · Physics C: Mechanics · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

A thin rod of length

L

has a linear mass density given by

\lambda(x)=\lambda_0\,\dfrac{x}{L}

, where

x

is measured from one end of the rod. Find the moment of inertia of the rod about the same end, expressed in terms of its total mass

M

and length

L

. (a)

\dfrac{2}{3}ML^{2}

(b)

\dfrac{1}{4}ML^{2}

(c)

\dfrac{1}{2}ML^{2}

(d)

\dfrac{1}{3}ML^{2}