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Ch 13: Rotational Inertia & EnergyWorksheetSee all chapters

# Moment of Inertia of Systems

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Sections
Types of Motion & Energy
Parallel Axis Theorem
Intro to Rotational Kinetic Energy
Moment of Inertia of Systems
Conservation of Energy in Rolling Motion
Conservation of Energy with Rotation
Moment of Inertia via Integration
Energy of Rolling Motion
Moment of Inertia & Mass Distribution
Intro to Moment of Inertia
More Conservation of Energy Problems
Torque with Kinematic Equations
Rotational Dynamics with Two Motions
Rotational Dynamics of Rolling Motion

Example #1: Inertia of disc with point masses

Transcript

Now, these r's, we have to slow down for a little bit, these are the distances between the center the axis of rotation, which is in the center, and what the object is, little r is the distance between the object and the center and we already have these figured out here, it's 2 and 4 so the 2 kilogram has a 2 meter distance and the 3 kilogram has a 4 meter distance, okay? So, let's just do this real quick, this is going to be 8, this is going to be 3 times 16. So, that's 48 and this is going to be 80, okay? So, we have 8 plus 48 plus 80 and this is going to be 136, 136 kilograms meter squared, cool? That's it for this one, hopefully got it, let me know if you have any questions.

Practice: 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. Practice: 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. Practice: 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. 