Question

A mass of 1 kg is placed at (1m, 2m, 0). Another mass of 2 kg is placed at (3m, 3m, 0). Find the moment of inertial of both the masses about z-axis

Answer 1

Moment of inertia of both the masses about z-axis is 41kgm^2

◆ Since Z= 0, in both coordinates, we know both particles are in xy plane.

◆MOMENT OF INERTIA ,

I = m(r)^2.

◆MOMENT OF INERTIA IN Z AXIS,

will be found by r_

( r_ =r perpendicular ),

since particles are in xy plane.

I = m(r_)^2

◆Here, r_ =( x^2 + y^2)^1/2

◆At (1,2) ;

r_ = (1^2 + 2^2)^1/2 = 5^(1/2)

◆At (3,3);

r_ = (3^2 +3^2)^1/2 = 18^(1/2)

◆ Mass at (1,2) is 1

Moment of inertia I" = m(r_)^2 = 1×【5^(1/2)^2 = 5kgm^2

◆Mass at (3,3) is 2

Moment of inertia I'= m(r_)^2 =2× 18 = 36kgm^2

◆ Total Moment of inertia I = I' + I" = 36 + 5 =41 kgm^2