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Find the moment of inertia of a mass of ...

Find the moment of inertia of a mass of 5 kg and another mass 10 kg about an axis of rotation which is 0.2 m from the 5 kg mass and 0.4 m from the 10 kg mass. Find the radius of gyration for the system.

Text Solution

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Moment of inertia `I = m_(1)r_(1)^(2) + m_(2)r_(2)^(2)`
`I = 5 xx (0.2)^(2) + 10 xx (0.4)^(2)`
`I = (5 xx 0.04) + (10 xx 0.16)`
`I = (0.20 + 1.6) = 1.8 kgm^(2)`
`Mk^(2) = 1.8` (k is the radius of gyration of the system)
`k^(2) = (1.8)/((10+5))=(1.8)/(15) = 0.12`
`k = sqrt(0.12) = 0.35 m (or) 35 cm`
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