# Moment of Inertia of Systems - Video Tutorials & Practice Problems

## Inertia of disc with point masses

You build a wheel out of a thin circular hoop of mass 5 kg and radius 3 m, and two thin rods of mass 2 kg and 6 m in length, as shown below. Calculate the system's moment of inertia about a central axis, perpendicular to the hoop.

^{2}

^{2}

^{2}

^{2}

A composite disc is built from a solid disc and a concentric, thick-walled hoop, as shown below. The inner disc (solid) has mass 4 kg and radius 2 m. The outer disc (thick-walled) has mass 5 kg, inner radius 2 m, and outer radius 3 m. Calculate the moment of inertia of this composite disc about a central axis perpendicular to the discs.

^{2}

^{2}

^{2}

^{2}

Three small objects, all of mass 1 kg, are arranged as an equilateral triangle of sides 3 m in length, as shown. The left-most object is on (0m, 0m). Calculate the moment of inertia of the system if it spins about the (a) X axis; (b) Y axis.

_{x}= 6.8 kg•m

^{2};

(b) I

_{y}= 4.5 kg•m

^{2}

_{x}= 18 kg•m

^{2};

(b) I

_{y}= 11.3 kg•m

^{2}

_{x}= 9.0 kg•m

^{2};

(b) I

_{y}= 18 kg•m

^{2}

_{x}= 6.8 kg•m

^{2};

(b) I

_{y}= 11.3 kg•m

^{2}

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