Figure 10.31 shows an object of mass M with one axis through its center of mass and a parallel axis through an arbitrary point A. Both axes are perpendicular to the page. The figure shows an arbitrary mass element dm and vectors connecting the center of mass, A, and dm. (a) Use the law of cosines (Appendix A) to show that (b) Use this result in to calculate the objects rotational inertia about the axis through A. Each term in your expression for leads to a separate integral. Identify one as the rotational inertia about the CM, another as the quantity and argue that the third is zero. Your result is a statement of the parallel-axis theorem (Equation 10.17).

Physics 211 – General Physics I Lecture 1.1 – 1.2 Useful formulas Displacement: Δx = x final initial Time Intervals: Δt = tfinal initial Avg Velocity: v av Δx/Δt Instantaneous Velocity – how fast the position (displacement) is changing at a certain...