Calculus Question

Question

Which is the moment of inertia of the following system about the x-axis 

 

m1 = 4 at (1, -3)

 

m2 = 7 at (3, 5)

 

m3 = 9 at (-3, 9)

Answer 1

The distances of the particles from the x-axis are r₁ = 3, r₂ = 5, r₃ = 9.

 

Thus the moment of inertial of the system is m₁r₁² + m₂r₂² + m₃r₃² = 4·3² + 7·5² + 9·9² = 36 + 175 + 729 = 940.

Answer 2

The mass moment or inertia equals I = ∫_mr²dm it is the second moment of mass about an axis r. With discrete masses and an axis, say x in a two dimentional frame, as in your problem this becomes ∑mi*yi^{^2} = 9*4 + 25*7 + 81*9 = 940 mr² or 940 lbs-sec-ft in the English system.