Question

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

Answer 1

Answer:

$I_{AB} = 7 kgm^2\\\\Radius \  \ of \ Gyration \ k = 0.84m$

Please check the attached pic for the answer

Answer 2

moment of inertia about AB is 7 kgm² and radius of gyration is √(0.7) m

there are four point masses 1kg, 2kg, 3kg and 4kg are located at the corners A, B , C and D respectively of a square ABCD of side 1m as shown in figure.

now momentum of inertis about AB , I = $m_Ar_A^2+m_Br_B^2+m_Cr_C^2+m_Dr_D^2$

= (1kg)(0)² + (2kg)(0)² + (3kg)(1m)² + (4kg)(1m)²

= 0 + 0 + 3 kgm² + 4kgm²

= 7 kgm²

now let radius of gyration is r

so, (1 kg + 2kg + 3kg + 4kg)r² = I = 7kgm²

⇒10r² = 7

⇒r = √(0.7) m

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