How Do You Calculate the Moment of Inertia for Different Shapes in Physics?

AI Thread Summary
The discussion focuses on calculating the moment of inertia for two different shapes: a tetrahedron made of four identical spheres and a T-shaped structure formed by two square slabs. For the tetrahedron, the user attempts to calculate the moment of inertia but realizes their method is incorrect and seeks clarification. Similarly, for the T-shaped slabs, the initial calculation is also deemed incorrect, prompting a request for assistance. The user asks for the correct equations for the moment of inertia for point masses and rectangles. Accurate formulas are essential for resolving these calculations effectively.
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1. Four small balls of identical mass 2.36 kg are arranged in a rigid structure as a regular tetrahedron. (A regular tetrahedron has four faces, each of which is an equilateral triangle.) Each edge of the tetrahedron has length 3.20 m. What is the moment of inertia of the system, for an axis of rotation passing perpendicularly through the center of one of the faces of the tetrahedron?

So we need to find moment of inertia for spheres

(7/5)(2.36)(3.20)=10.57 (This isn't correct so i don't know what to do

2. Two thin, square slabs of metal, each with side length of 0.34 m and mass 0.29 kg, are welded together in a T shape and rotated on an axis through their line of intersection. What is the moment of inertia of the T?

So we need to find moment of inertia for slabs

(1/12)(0.29)(0.34)=.00279 (this is not correct)

Can someone correct me on these two problems
 
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1. What is the equation for moment of inertia of a collection of pointlike masses?

2. What is the equation for moment of inertia of a rectangle?
 
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