You are a project manager for a manufacturing company. One of the machine parts

Question

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 0.900 kg .

i. What is the moment of inertia of this rod for an axis at its center, perpendicular to the rod?

ii. 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?

Explanation / Answer

here,

mass , m = 0.9 kg

length , l = 0.6 m

1)

the moment of inertia of this rod for an axis at its center , I = m * l^2/12

I = 0.9 * 0.6^2 /12

I = 0.027 kg.m^2

the moment of inertia of this rod for an axis at its center is 0.027 kg.m^2

2)

theta = 60 degree

the moment of inertia of this bent rod about an axis perpendicular to the plane of the V at its vertex , I' = 2 * ( (m/2) * (l/2)^2) /3

I' = 2 * (0.45 * 0.3^2 ) /3

I' = 0.027 kg.m^2

the moment of inertia of this bent rod about an axis perpendicular to the plane of the V at its vertex is 0.027 kg.m^2

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