6.3.2 Calculating the Rotational Inertia of Solid Bodies

Question 1

Calculating the Rotational Inertia of Solid Bodies

Answer 1

• The moment of inertia of a system of point masses:
• The moment of inertia of a continuous mass distribution:
• Given the moment of inertia of an object around an axis through its center of mass , the moment of inertia around aparallel axis is found using the parallel-axis theorem:

Question 2

Which of the following statements concerning the moment of inertia I is false?

Answer 2

The moment of inertia depends on the angular acceleration of the object as it rotates.

Question 3

Which of the following is the moment of inertia of a thin hoop of radius r ? The axis goes through the rim of the hoop, perpendicular to the plane of the hoop.

Answer 3

2mr ^2

Question 4

Two uniform solid spheres of mass m and radius r are connected by a thin (massless) rod of length 8r so that the centers are 4r from the axis of rotation, as the design model for a space station that is to have artificial gravity. Which of the following is the moment of inertia of this system about an axis perpendicular to the rod at its center?

Answer 4

164mr^2/5

Question 5

A crucial piece of a machine starts as a flat uniform cylindrical disk of radius R and mass m. A circular hole with radius r is then drilled into it. The hole’s center is a distance h from the center of the disk. Which of the following is the moment of inertia of this disk with an off-center hole when rotated about its center of mass?

Answer 5

1/2m(R^2-r^2)

Question 6

Three objects are attached to a massless rigid rod as shown. Assuming point masses, which of the following is the moment of inertia?

Answer 6

7 kg • m^2

Question 7

Which of the following masses contributes most to the moment of inertia?

Answer 7

The 1 kg mass

Question 8

A massless frame in the shape of a square with sides of length r (in meters) has a ball with a mass of m (in kg) at each corner. What is the moment of inertia of the four balls about an axis through the corner marked X and perpendicular to the place of the paper?

Answer 8

4mr^ 2

Question 9

Calculate the moment of inertia of a long thin rod (mass m and length l) with a linear mass density that increases as the square of the distance from the axis at one end of the rod.

Answer 9

3/5 ml^2