Question

What happens to the moment of inertia of a cylinder if we half its mass and double its radius? Enter a number that expresses the new inertia in terms of the old

Answer 1

Assuming your question is about solid cylinder

The Moment of Inertial of cylinder with Mass M and Radius R along its axis is given by

$\frac{1}{2}MR^{2}$

Let initial Moment of Inertia be I₀

$I_0= \frac{1}{2}MR^{2}$

Now Mass is reduced to half and Radius is doubled

Let new Moment of inertia be I_new

$I_{new}= \frac{1}{2}\frac{M}{2}(2R)^{2}$

Incw = 2 x 10

$\frac{I_{new}}{I_{0}}= 2$