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 cm long and has mass0.600 kg .

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

2) 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.

Explanation / Answer

length of the rod l=60 cm

mass m=0.6 kg

A)

moment of inertia of given thin rod about axis passing through centre and perpendicular to its length is,

I=(1/12)*m*l*2

I=(1/12)*0.6*(0.6)^2

I=1.8*10^-2 kg.m^2

B)

now,

moment of Inertia of the one rod is,

I1=1/3*(m/2)*(l/2)^2

and

moment of Inertia of the second rod is,

I2=1/3*(m/2)*(l/2)^2

total moment of inertia I=I1+I2

I=1/3*(m/2)*(l/2)^2 + 1/3*(m/2)*(l/2)^2

I=m*l^2/24 + m*l^2/24

I=m*l^2/12

I=(1/12)*0.6*(0.6)^2

I=1.8*10^-2 kg.m^2

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