Question 366: Centre of Mass and Rotational Motion

Question

Consider a uniform square plate of side $$' a '$$ and mass $$'m'$$. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

Accepted Answer

Moment of inertia for the square plate through O, perpendicular to the plate is
$${I_{nn'}} = {1 \over {12}}m\left( {{a^2} + {a^2}} ight) = {{m{a^2}} \over 6}$$
Also, $$DO = {{DB} \over 2} = {{\sqrt 2 a} \over 2} = {a \over {\sqrt 2 }}$$
According to parallel axis theorem
$${{\mathop{m I}
olimits} _{mm'}} = {I_{nn'}} + m{\left( {{a \over {\sqrt 2 }}} ight)^2}$$
$$ = {{m{a^2}} \over 6} + {{m{a^2}} \over 2} $$
$$= {{m{a^2} + 3m{a^2}} \over 6} $$
$$= {2 \over 3}m{a^2}$$

Answer

$${5 \over 6}m{a^2}$$

Answer

$${1 \over 12}m{a^2}$$

Answer

$${7 \over 12}m{a^2}$$

Answer

$${2 \over 3}m{a^2}$$

Centre of Mass and Rotational Motion

Consider a uniform square plate of side $' a ' and mass 'm'$. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

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