Question 6 of 15 Incorrect Map Sapling Learning macmillan learning A thin rod of

Question

Question 6 of 15 Incorrect Map Sapling Learning macmillan learning A thin rod of length L is placed along the x axis with its center at the origin, as shown in the figure. The rod has a total mass M, which is distributed along its length according to the linear mass density (x) 7 where A is a constant with units of kg/m Find an expression for A in terms of M, L and any whole numbers 448M -L/2 0 L/2 Calculate ly, the moment of inertia of this rod about the y axis. Answer with the numerical coefficent of ML Incorrect. The general formula for the moment of inertia about some axis is Number I-0.14 ML where r is the distance from the differential mass element dm to the rotation axis. The integration is performed over the entire length of the rod. You can express dm in terms of and dx as you did in solving for the constant A Previous Give Up & View SolutionTry Again Next Exit

Explanation / Answer

M = 2 Ax6dx from 0 to L/2

M = 2/7 * Ax7 from 0 to L/2

M = 2/7 * A * (L/2)7= AL7 / 448

so

A = 448M / L7

I = 2 Ax6 * x² dx from 0 to L/2

I = 2/9* A * x9 from 0 to L/2

I = 2/9* A * (L/2)9 = AL9 / 2304

Substitute for A:

I =0.192ML2

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