|

Mechanics

Blazing goIITian

 Joined: 8 Dec 2006 Post: 351
9 Jun 2007 15:20:36 IST
0 People liked this
1
408
a fundamental query
Engineering Entrance , Medical Entrance , AIPMT , JEE Main , AIIMS , JEE Advanced , Physics , Mechanics

while finding the moment of inertia of a body frm an axis why do we integrate r^2 dm and not any other value of r ?why is the distance from the axis of rotation chosen as r^2?

Blazing goIITian

Joined: 18 Feb 2007
Posts: 1042
9 Jun 2007 16:55:16 IST
1 people liked this

see
first of all let us see the definition of moment of inertia
now i will do this with the help of an example
for eg: we have to find the kinetic energy of a circular body rotating about it's centre of mass with angular velocity w(omega)
now total kinetic energy = sum of kinetic energy of all particles
= 1/2m1v12 + 1/2m2v22 + 1/2m3v32 ..............
= 1/2m1r12w2 + 1/2m2r22w2 + 1/2m3r32w2...........          (as v = rw where r is the distance of the particle from axis of rotation(centre of mass in this case).
=1/2(m1r12 + m2r22 +m3r32 ...........) * w2
1/2 * I * w2
therefore we see that I i.e moment of inertia about an axis is the sum of products of the mass of the particles and square of thier distance  from that axis  (centre of mass in this case)  (definition)

So when we integrating we take a small particle of mass dm & measure it's distance from the axis chosen & then square it therefore the integral becomes  r2dm
therefore it is now clear from definition that r is always the distance of the particle of mass dm from the axis and not some other arbitrary r
I HOPE I'VE CLEARED YOUR DOUBT
CHEERS

 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

## For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 9960 m Post - 2185
4. edison
 Altitude - 10815 m Post - 7797
5. Sagar Saxena
 Altitude - 8625 m Post - 8064
 Altitude - 6330 m Post - 1979

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone