A uniform thin square plate of side and mass is placed with its centre at the origin…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

A uniform thin square plate

ABCD

of side

0.20\,\text{m}

and mass

1.5\,\text{kg}

is placed with its centre

O

at the origin in the

xy

–plane so that its sides are parallel to the coordinate axes. (a) Find the moments of inertia

I_x

and

I_y

of the plate about the

x

– and

y

–axes through

O

. Express each answer numerically. (b) Hence obtain the moment of inertia

I_O

about the axis through

O

perpendicular to the plate. (c) Determine the moment of inertia

I_P

of the plate about a parallel axis perpendicular to the plate that passes through the corner

A

. State your final answer correct to two significant figures.