consider the system of three bodies of masses 1kg,2kg and 3kg are at the position of i+j m, 2i+2j m and 2i+3j m respectively. what is the moment of inertia of the system from the axis passing through its centre of mass and parellel to z axis
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Answer:
Required M.O.I = 4.16 kg m²
Explanation:
Co-ordinates of CM are
r(x,y) = ∑mr/M
= 1(1, 1) +2(2, 2) + 3 (2, 3)/6
= (11/6 , 14/6)
M.O.I about Origin in along z axis
Iz = ∑m (x²+y²)
= 1 ( 1² + 1²) + 2(2²+2²) + 3 (2² + 3²)
= 2 + 16 + 39
®= 57 kg m²
M.O.I about centre of mass and parallel to z axis is
Ig =Iz - Mk²
= 57 - 6 x {[11/6)² + (14/6)²}
= 57 - 6{ 121/36 + 196/36}
= 57 - (6 x 317)/36
= 57 - 317/6
= 342 - 317/6
= 25/6
= 4.16 kg m²
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