A uniform disc and hollow right circular cone have the same formula for their moment of inertia when rotating about the central axis why is it so?

Question

asked Jan 27, 2021 66.5k views

1 Answer

Dreaddan · Answer 1 · 2021-02-01T14:37:09+0000

Answer:

This is as a result that about the central axis a collapsed hollow cone is equivalent to a uniform disc

Step-by-step explanation:

The integration of the differential mass of the hollow right circular cone yields

$I=\int\limits dmr^2 = \int\limits^a_b {(2Mxr^2)/(R^2 +H^2) } \, dx = (2MR^2dx)/((R^2 +H^2)^2) ((R^2 +H^2)^2)/(4) = (1)/(2)MR^2$

and for a uniform disc

I = 1/2πρtr⁴ = 1/2Mr².