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

[Ion1776]

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

 

[Redbelly98]

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?

 

[tomcue]

?

I would suggest first checking your calculations and units to ensure they are correct. For the first problem, the moment of inertia for a sphere is given by I = (2/5)mr^2, where m is the mass and r is the distance from the axis of rotation. Since the spheres are arranged in a regular tetrahedron, the distance from the axis of rotation to the center of mass of each sphere is (3.20/2) = 1.60 m. So, the moment of inertia for one sphere would be I = (2/5)(2.36)(1.60)^2 = 3.80 kgm^2. Since there are four spheres, the total moment of inertia for the system would be 4(3.80) = 15.20 kgm^2.

For the second problem, the moment of inertia for a rectangular slab is given by I = (1/12)ml^2, where m is the mass and l is the length of one side. Since the two slabs are welded together in a T shape, the moment of inertia would be the sum of the individual moments of inertia for each slab. So, I = (1/12)(0.29)(0.34)^2 + (1/12)(0.29)(0.34)^2 = 0.00279 kgm^2.

I would also suggest checking with your teacher or classmates for clarification on the problem and any specific equations or concepts that may be relevant. It is always important to double check your work and seek help when needed to ensure accuracy in scientific calculations.