Question

Four point masses $1$ kg, $2$ kg, $3$ kg and $4$ kg are located at the corners A, B, C and D respectively of a square ABCD of side $1$ m. Find the moment of inertia and radius of gyration of the system about AB as the axis of rotation.

Answer 1

axis of rotation is $AB$

It is a discrete mass system. We should Individually calculate Moment of Inertia

$r=$ Distance of particle from axis of rotation

for $1kg$ particle $\Rightarrow I_A=1\times r^2=0$ ( as $r$ for $1kg$ is $0$ as it lies on axis)

for $2kg$ particle $\Rightarrow I_B=2\times r^2=0$

for $4kg$ $\Rightarrow I_D=4\times 1^2=4kg{m}^2$

for $2kg$ $\Rightarrow I_C=3\times 1^2=3kg{m}^2$

So total moment of Inertia $=0+0+4+3$

$I=7kg{m}^2$

Radius of gyration $\left(K\right)=\sqrt{\frac{I}{Totalmass}}$

$K=\sqrt{\frac{7}{10}}$

$K=\sqrt{\frac{7}{10}}m$.