what happens to moment of inertia?

Classical Mechanics Level 1

A metal ring is melted and a solid sphere is made out of it. What happens to the moment of inertia about the vertical axis through the center?

Moment of inertia increases Moment of inertia remains the same as the total mass remains the same Moment of inertia decreases due to the decrease in the distance of the redistributed mass Not enough information

Vivek Vijayan by vivek vijayan , 26, India

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5 solutions

Vivek Vijayan
Apr 10, 2014

distance from center and the extreme point on the surface decrease, so M.I decreases.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I doubt if that is the reason. It is because some part of mass are distributed closer to axis which makes its MI less

Shuvam Nayak - 7 years, 1 month ago
Suganthan Venkat
May 2, 2018

we know the moment of inertia is dependent of mass and distances,as the mass are same for both solid sphere and metal ring,distance of the mass distribution are different and more in metal ring

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Koustav Chandra
Aug 20, 2017

We know I=MR^2 where I=sum of M.I., M=total mass, R=distance of mass from the center. When Mass is redistributed R decreases so M.I. decreases.

2 Helpful 0 Interesting 0 Brilliant 1 Confused
Bodh Nath Prasad
May 26, 2019

Because the radius of rotation reduces.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
M. Siddique
May 23, 2017

More Mass distributed Near The axis of rotation, less effort will that require. Because Inertia = Sum of mass X Sum of Square of its Distance from axis of rotation

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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