Answer to Question #324073 in Mechanics | Relativity for Rupal

Question

Find the moment of inertia of a circular disc (i) about an axis through its center and perpendicular

to its plane (ii) about a diameter.

Answer 1

Explanations & Calculations

• The moment of inertia of a circular disk about its central axis perpendicular to its plane is given by

$\qquad\qquad \begin{aligned} \small I_{c}&=\small \frac{1}{2}mr^2 \end{aligned}$

• Then the moment of inertia about one of its diameters $\small (I_d)$ can be found using the parallel axis theorem which is for XYZ 3D plane, $\small I_z=I_x+I_y$.
• Then,

$\qquad\qquad \begin{aligned} \small I_c&=\small I_d+I_d\\ \small I_d&=\small \frac{I_c}{2}\\ &=\small \frac{1}{4}mr^2 \end{aligned}$