Moment of inertia for a point mass:

$\overline{){\mathbf{I}}{\mathbf{=}}{\mathbf{M}}{{\mathbf{R}}}^{{\mathbf{2}}}}$

Moment of inertia of a solid sphere:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{2}}{\mathbf{5}}{\mathbf{M}}{{\mathbf{R}}}^{{\mathbf{2}}}}$

Moment of inertia of a rod about the end:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{3}}{\mathbf{M}}{{\mathbf{L}}}^{{\mathbf{2}}}}$

Newton's second law for the angular motion:

$\overline{){\mathbf{\tau}}{\mathbf{=}}{\mathbf{I}}{\mathbf{\alpha}}}$, where τ is the net external torque, I is the moment of inertia, and α is the angular acceleration.

Torque:

$\overline{){\mathbf{\tau}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\times}}{\mathbf{F}}}$

An object is formed by attaching a uniform, thin rod with a mass of m_{r} = 6.85 kg and length L = 5.76 m to a uniform sphere with mass m_{s} = 34.25 kg and radius R = 1.44 m. Note m_{s} = 5m_{r} and L = 4R.

1) What is the moment of inertia of the object about an axis at the left end of the rod?

kg-m^{2}

2) If the object is fixed at the left end of the rod, what is the angular acceleration if a force F = 460 N is exerted perpendicular to the rod at the center of the rod?

rad/s^{2}

3) What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)

kg-m^{2}

4) If the object is fixed at the center of mass, what is the angular acceleration if a force F = 460 N is exerted parallel to the rod at the end of rod?

rad/s^{2}

5) What is the moment of inertia of the object about an axis at the right edge of the sphere?

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