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System of Particles and Rotational Motion

Moment of inertia

Find the moment of inertia of the {rod} A B about an axis yy a

Question

Medium

Solving time: 3 mins

Find the moment of inertia of the $rod A B$ about an axis yy as shown in figure. Mass of the rod is $m$ and length is $l$ .

Views: 5,367 students

Book:

Mechanics Volume 2 (DC Pandey)

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Eleanor Discussed

Find the moment of inertia of the

rod A B

about an axis yy as shown in figure. Mass of the rod is

m

and length is

l

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Mass per unit length of the rod

= \frac{m}{l}

Mass of an element

PQ

of the rod is,

d m = (\frac{m}{l}) d x

Perpendicular distance of this elemental mass about

yy

is,

r = x sin α

∴

Moment of inertia of this small element of the rod (can be assumed as a point mass) about

yy

is,

d I = (d m) r^{2} = (\frac{m}{l} d x) (x sin α)^{2} = (\frac{m}{l} sin^{2} α) x^{2} d x

∴

Moment of inertia of the complete rod,

I = \int_{x = 0}^{x = l} d I = \frac{m}{l} sin^{2} α \int_{0}^{l} x^{2} d x = \frac{m l ^{2}}{3} sin^{2} α

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Question Text	Find the moment of inertia of the $rod A B$ about an axis yy as shown in figure. Mass of the rod is $m$ and length is $l$ .
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	93

Find the moment of inertia of the $rod A B$ about an axis yy as shown in figure. Mass of the rod is $m$ and length is $l$ .

Text solutionVerified

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Find the moment of inertia of the $rod A B$ about an axis yy as shown in figure. Mass of the rod is $m$ and length is $l$ .