Exercise 9.32 : You are a project manager for a manufacturing company. One of th

Question

Exercise 9.32 : You are a project manager for a manufacturing company. One of the machine parts on the assembly line is a thin, uniform rod that is 60.0 cmlong and has mass 0.350 kg

(A) What is the moment of inertia of this rod for an axis at its center, perpendicular to the rod? Express your answer with the appropriate units.

I = ?

(B) One of your engineers has proposed to reduce the moment of inertia by bending the rod at its center into a V-shape, with a 60.0 angle at its vertex. What would be the moment of inertia of this bent rod about an axis perpendicular to the plane of the V at its vertex? Express your answer with the appropriate units.

I = ?

I have no idea how to start this, so explanations for each step are greatly appreciated. Thank you!!

Explanation / Answer

(A) I = 1/12 mL^2 = 1/12 *0.35*0.6^2 = 0.0105 kg m^2

(B) we can view this V shape as two rod rotate by their ends, I = 1/3 mL^2 for rod ratate about its ends,

thus I = 2*1/3 * (m/2) (L/2)^2 = 2/3 * 0.350/2 * 0.3^2 =0.0105 kg m^2,

its moment of inertia does not change by bending

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