A uniform lamina lies entirely in the –plane with its centre at the origin.

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A uniform lamina lies entirely in the

xy

–plane with its centre at the origin. (a) State the relation connecting the moments of inertia

I_x, I_y

(about the

x

– and

y

–axes through the origin) with the moment of inertia

I_z

(about the axis through the origin perpendicular to the plane). (b) Give one clear reason why the relation obtained in part (a) cannot be applied to a solid sphere of the same mass and radius. (c) A thin circular disc of mass

M

and radius

R

lies in the

xy

–plane with its centre at the origin. Using symmetry arguments only, find the numerical ratios

I_x\text{:}I_y\text{:}I_z

for the disc.

Related theory

Rigid Body Motion
Moment of Inertia
Rotational dynamics

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