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Mechanics

Cool goIITian

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23 Mar 2008 21:57:15 IST

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544

rotation

None

a thin uniform rod of mass m and length l rotates with constant angular velocity omega about the vertical axis passing through the rod's suspension point O. In doing so the rod describes a conical surface with half aperture angle 'theta'.

what is the component of reaction force at O in x direction?

and magnitude of angular momentum of rod about axis of rotation ?

ans;

1. ml

² / 2

2. ml²

/ 12

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Comments (8)

Sairam

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24 Mar 2008 01:30:00 IST

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If the radius of the circle at the bottom u have drawn is also l, then d ans is rt.
if so,
Centre of mass of rod rotates in a circle of radius l/2.
Force for this can be provided only by the horizontal component of hinge force.
m

²l/2 is the centripetal force, n this is equal to horizontal component of hinge force.

I dont think magnitude of angular momentum is m

l²/12.

BALGANESH

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24 Mar 2008 02:17:10 IST

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elastiboysai if it rotates with a radius of l then it won't become a conical pendulum

as far as ans are concerned i think they are wrong

2) calculating MOI alon O ml^2/12 ml^2/4

=ml^2/ 3

ml^2/3

anchit saini

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Posts: 1251

24 Mar 2008 02:20:32 IST

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well balganesh
I is not ml^2 / 3

if u notice the axis is passing through the end but is not perpendicular to it

sharmadon

Cool goIITian

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24 Mar 2008 10:50:42 IST

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yes balganesh..the answer by u isnt correct...

ankita DESHMUKH

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24 Mar 2008 11:44:38 IST

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let da force thru da rod b T ............

da radius of the circle described by da rod at da bottom wud b = l sin theta

T sin

= m

²l sin

T cos

= mg

T = m

²l

dis wud b da reaction force exerted at o
its component in x direction m

²l sin

.

2)
moi = ml²/3 sin

angular momentum = ml²/3 sin

Siddhant Shah

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24 Mar 2008 20:28:55 IST

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@ anki016-

Are you sure components of the moment of inertia can be taken?

Can u plz validate ur point through some theorem probably??

Sairam

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24 Mar 2008 20:30:50 IST

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sid anki has merely said the radius of circle described=lsin

its not I

Siddhant Shah

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Posts: 369

24 Mar 2008 20:35:20 IST

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No elasti, not the radius, I'm talking about the second part

MoI = ml2/3sin@

that one......

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