Problem 1. Three particles are distributed in the x-y plane as shown in the figure.

•  Find the moment of inertia about an axis that passes through the center of coordinate system.

•  Find the moment of inertia about an axis that passes through particle 1.

 

 

Problem 2. A particle of mass 2 kg is attached to a thin uniform rod of mass 6 kg and length 1 m as shown in the figure. Find the moment of inertia about axis O.

 

Problem 3. A thin disk with a circular hole at its center, called an annulus, has inner radius 10 cm and outer radius 30 cm. The mass of the disk is 2 kg.

(a) Find the moment of inertia of the disk about the axis through the center of the disk.

(b) Find the moment of inertia of the disk about the axis through the edge of the disk.

 

Problem 4. A particle of mass 400 g is attached to a uniform thin disk of radius 40 cm. The particle is at distance 20 cm from the center of the disk. The mass of the disk is 1 kg. Find the moment of inertia of the system about the axis through the center of the disk.

 

Problem 5. A thin rod of mass 2 kg and length 30 cm is attached to a uniform disk of radius 50 cm and mass 4 kg as shown in the figure. Find the moment of inertia about the axis through the center of the disk.

 

Problem 6. Four particles of mass 300 g each are connected by four rods, which form the sides of the square, as shown in the figure. The rods have the same mass 500 g and the same length 30 cm.

Find the moment of inertia about the axis through the center of the square.