Question 466: Centre of Mass and Rotational Motion

Question

A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is _______ $$	imes$$ 10
$$-$$1
kg m
2
.

Accepted Answer

MOI of AB about $$P:{I_{ABp}} = {{{M \over 6}{{\left( {{l \over 6}} ight)}^2}} \over {12}}$$
MOI of AB about O,
$${I_{A{B_O}}} = \left[ {{{{M \over 6}{{\left( {{l \over 6}} ight)}^2}} \over {12}} + {M \over 6}{{\left( {{l \over 6}{{\sqrt 3 } \over 2}} ight)}^2}} ight]$$
$${I_{Hexago{n_0}}} = 6{I_{A{B_0}}} = M\left[ {{{{l^2}} \over {12 	imes 36}} + {{{l^2}} \over {36}} 	imes {3 \over 4}} ight]$$
$$ = {6 \over {100}}\left[ {{{24 	imes 24} \over {12 	imes 36}} + {{24 	imes 24} \over {36}} 	imes {3 \over 4}} ight]$$
= 0.8 kgm
2
= 8 $$	imes$$ 10
$$-$$1
kg-m
2

Centre of Mass and Rotational Motion

A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is _______ $\times 10 -$1 kg m 2 .

Integer / Numeric Answer Type