Q32E You are a project manager for a ... [FREE SOLUTION]

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University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Physics

14th edition Edition 路 1596 pages

ISBN: 9780321973610

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 $0.012 k g . m^{2}$ .

Perpendicular to the plane of the V at its vertex is $\frac{m l^{2}}{12}$ .

Step by step solution

Step:-1 expression

Given m =0.400 and

l =0.600

Step:-2 Concept

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

hence we know the moment of inertia formula is

$\frac{m l^{2}}{12}$ _____(1)

Step:-3 calculation

Put the value in equation (1)

$\frac{m l^{2}}{12} = \frac{0.400 kg 脳 (0.600 m)}{12} = \frac{0.400 脳 0.36}{12} = \frac{0.144}{12} = 0.012 kg 鈰� m^{2}$

Step:-4 expression

We know that,two rods each having ,

Mass= $\frac{m}{2}$

Length = $\frac{l}{2}$

Step:-5 Concept

we know that definition $I_{t o t a l} = \frac{2 m l}{3}$

we also know that the formula $m = \frac{m}{2}$

and formula of $L = \frac{l}{2}$

Step:-6 calculation

Put the value in the expression,

$l_{t o t a l} = \frac{2 (\frac{m}{2}) {(\frac{l}{2})}^{2}}{3} = \frac{m l^{2}}{12}$

The distribution of mass about the axis of rotation is $\frac{m l^{2}}{12}$ .

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Short Answer

Step by step solution

Step:-1 expression

Step:-2 Concept

Step:-3 calculation

Step:-4 expression

Step:-5 Concept

Step:-6 calculation

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