Question

The masses and coordinates of four particles are as follows: 40 g, x = 3.0 cm, y = 2.0 cm; 25 g, x = 0.0 cm, y = 4.0 cm; 50 g, x = -3.0 cm, y = -3.0 cm, 30 g, x = -2.0 cm, y = 4.0 cm.

A)What is the rotational inertia of this collection with aspect to the x-axis ( kg m²)?

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

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

Answer 1

moment of inertia about an axis is given by mass*r^2

where r=perpendicular distance to that axis.

if coordinates of a particle is (x,y),

perpendicular distance from x axis=y

perpendicular distance from y axis=x

perpendicular distance from z axis=sqrt(x^2+y^2)

part a:

rotational inertia about x axis

=(0.04*0.02^2) + (0.025*0.04^2) + (0.05*0.03^2) + (0.03*0.04^2)=1.49*10^(-4) kg.m^2

part b:

rotational inertia about y axis

==(0.04*0.03^2) + (0.025*0^2) + (0.05*0.03^2) + (0.03*0.02^2)=9.3*10^(-5) kg.m^2

part c:

rotational inertia about z axis

=(0.04(*0.03^2+0.02^2)) + (0.025*(0^2+0.04^2)) + (0.05*(0.03^2+0.03^2)) + (0.03*(0.02^2+0.04^2))=2.42*10^(-4) kg.m^2