Four particles, each of mass 1 kg are placed at four corners of a square of side 2 m . The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its verte

Question

Four particles, each of mass 1 kg are placed at four corners of a square of side 2 m . The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertex is _ _ _ _ _ _ kg m 2 .

TestHub · Accepted Answer

The formula to calculate the moment of inertia of a system of particles about a point can be written as

$I = \sum_{i = 1}^{n} m_{i} r_{i}^{2} . . . (1)$

where, $m_{i}$ is the mass of the $i^{th}$ particle situated at a distance $r_{i}$ from the point.

With reference to the above diagram, it can be written that the net moment of inertia of the system of particles is

$\begin{array}{rcl} I & = & m a^{2} + m a^{2} + m (\sqrt{2} a)^{2} \\ = & 4 m a^{2} \\ = & 4 \times 1 kg \times {(2 m)}^{2} \\ = & 16 kg m^{2} \end{array}$

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