Home » Ask & Discuss » Physics. » Mechanics « Back to Discussion

Mechanics

Scorching goIITian

Joined:	16 Dec 2006
Post:	214

11 Nov 2007 21:03:45 IST

0 People liked this

413

Moment OF inertia

None

Three Identical Rods, each of the length L,are joined to form a rigid Equilateral triangle its radus of gyration about an axis passing through a corner and perpendicular to the plane of the triange is:

Pls DO answer

Share this article on:

Comments (4)

nishant singh

Blazing goIITian

Joined: 23 Feb 2007

Posts: 424

11 Nov 2007 21:15:46 IST

Like 2 people liked this

Find Moment of Inertia of the system about that point
let that point be intersectionbe'P' of rod L1,L2;;;;; L3 is rod oppsite to point

moment of inertia of L1 about P = ML^2/3
M.I of L2 about P = ML^2/3
M.I of L3 about P = ML^2/12 + M(

3L/2)^2 {used parallel axis theorem distance of centre of mass of L3 from P }

thus m.I about P = 2ML^2/3 + ML^2/12 + 3ML^2/4
18ML^2/12 = 3ML^2/2

k be radius of gyration

3Mk^2 = 3ML^2/2
k =

(L^2)/2
k= L/

2

do rate me if correct:)

Karthik M

Blazing goIITian

Joined: 1 May 2007

Posts: 2830

11 Nov 2007 21:18:27 IST

Like 1 people liked this

Now the axis passes through one of the corners => it will be common to the corner of 2 rods.

So, moment of inertia of these 2 rods = 2/3ml²

Consider the third rod :

The moment of inertia of the third rod about its center is ml²/12.

the distance of the center of the rod from the corner =

3l/2

Using parallel axis theorem, MI of this rod about the corner

= ml²/12 + 3ml²/4 = 10ml²/12.

So net moment of inertia = 2/3ml² + 10ml²/12
= 18ml²/12.

To find radius of gyration:

Net mass of the system = 3m. Let radius of gyration be K.

Now we know that Moment of inertia = MK²

so 18ml²/12 = 3mK²

which gives K = l/

2

Hope that helped!

Cheers!

Krishna Gopal Singh

Forum Expert

Joined: 29 Dec 2006

Posts: 5153

11 Nov 2007 22:50:42 IST

Like 0 people liked this

Perfect answers nishant and Kartik

Rahul Karmakar

Scorching goIITian

Joined: 16 Dec 2006

Posts: 214

12 Nov 2007 13:20:38 IST

Like 0 people liked this

Thanks Guys !

I was Mistaking for the third rod's MI
Anyways Thanks for the Answer.

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team