The masses and coordinates of four particles are as follows

The masses and coordinates of four particles are as follows: 45 g, x = 1.0 cm, y = 1.0 cm; 30 g, x = 0.0 cm, y = 4.0 cm; 20 g, x = -3.0 cm, y = -3.0 cm, 50 g, x = -1.0cm, y = 3.0 cm. What is the rotational inertia of this collection with aspect to the x-axis ( kgm²)?

What is the rotational inertia of this collection with aspect to the y-axis?

What is the rotational inertia of this collection with aspect to the z-axis?

Solution

Ans :- the total moment of inertia for a rigid body consisting of N point masses Mi with distances Ri to the rotation axis equals the sum of the point-mass moments of inertia
I = Sum (Mi*Ri^2)

Along X- axis

Ix = M1*R1^2 +M2*R2^2 +M3*R3^2 +M4*R4^2

    =45*10^-3*(1*10^-2)^2 + 30*10^-3*(0)^2 +20*10^-3*(-3*10^-2)^2 + 50*10^-3*(-1*10^-2)^2

Ix = 2.75*10^-5kgm^2

Iy = 45*10^-3*(1*10^-2)^2 +30*10^-3*(4*10^-2)^2 +20*10^-3*(-3*10^-2)^2 + 50*10^-3*(3*10^-2)^2

Iy = 1.2 *10^-4Kgm^2

Iz =0Kgm^2