Concept #1: Parallel Axis Theorem

The moment of inertia of a 1.7 kg object about its center of mass is measured to be 150 kgm2. What would the moment of inertia be for a parallel axis 15 cm from the center of mass?

A smaller disk of mass 0.15 kg sits atop a larger disk of mass 0.5 kg as shown in the figure. If the system rotates about the axis shown with an angular speed of 150 rad/s, what is the moment of inertia of the system?

A massless rod of length L has a mass m fastened at one end and a mass 2m fastened at the other end. What is the ratio of the moment of inertia about an axis through the mass m to the moment of inertia through the center of the rod?
1. 3/2
2. 4/3
3. 3/4
4. 2
5. 8/3
6. 3/8
7. 2/3
8. 1/2

Find the moment of inertia of a solid sphere of mass M = 5 kg and radius R = 0.2 m about an axis that is tangent to the sphere.
1. 4.116
2. 0.28
3. 4.032
4. 0.441
5. 0.63
6. 0.504
7. 0.378
8. 2.52
9. 2.772
10. 0.448

Small blocks, each with mass m , are clamped at the ends and at the center of a rod of length L and negligible mass. Compute the moment of inertia of the system about an axis perpendicular to the rod and passing through:a) the center of the rodb) a point one-fourth of the length from one end

Find the moment of inertia of a hoop (a thin-walled, hollow ring) with mass exttip{M}{M} and radius exttip{R}{R} about an axis perpendicular to the hoops plane at an edge.

A thin, rectangular sheet of metal has mass M and sides of length a and b. Use the parallel-axis theorem to calculate the moment of inertia of the sheet for an axis that is perpendicular to the plane of the sheet and that passes through one corner of the sheet.