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Chapter 1: Q32E (page 296)

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 a mass of 0.400 kg.

(a) What is the moment of inertia of this rod for an axis at its center,

perpendicular to the rod?

(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 60.0o 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?

Short Answer

Expert verified

The moment of inertia is 0.012kg.m2.

Perpendicular to the plane of the V at its vertex is ml212.

Step by step solution

01

Step:-1 expression

Given m =0.400 and

l =0.600

02

Step:-2 Concept  

in the given question we need to find a moment of inertia.

hence we know the moment of inertia formula is

ml212_____(1)

03

Step:-3 calculation

Put the value in equation (1)

ml212=0.400kg脳(0.600m)12=0.400脳0.3612=0.14412=0.012kg鈰�m2

04

Step:-4 expression 

We know that,two rods each having ,

Mass=m2

Length =l2

05

Step:-5 Concept 

we know that definitionItotal=2ml3

we also know that the formulam=m2

and formula ofL=l2

06

Step:-6 calculation 

Put the value in the expression,

ltotal=2m2l223=ml212

The distribution of mass about the axis of rotation is ml212.

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Most popular questions from this chapter

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