Moment of Inertia for Three Point Masses

Click For Summary
SUMMARY

The discussion centers on calculating the moment of inertia for three point masses located at A=(-a, -a), B=(a, -a), and C=(0, a) with respect to an axis along the z-axis through the origin. The formula used is I = m((rA)² + (rB)² + (rC)²), leading to the calculation of I = 5ma². However, there is confusion as the expected answer is 4.12ma², prompting participants to question the source of the discrepancy.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with Cartesian coordinates
  • Basic knowledge of physics equations
  • Ability to perform square root and square calculations
NEXT STEPS
  • Review the derivation of moment of inertia for point masses
  • Investigate the differences in calculation methods for moment of inertia
  • Examine the reference material or textbook for potential errors
  • Learn about the impact of mass distribution on moment of inertia
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and moment of inertia calculations, as well as educators seeking to clarify concepts related to point mass systems.

atlantic
Messages
21
Reaction score
0

Homework Statement



Three particles of mass m are placed at A=(-a, -a), B=(a, -a) and C=(0, a)

Find the moment of inertia for an axis along the z-axis through the origin



Homework Equations



I = m((rA)2 + (rB)2 + (rC)2)



The Attempt at a Solution


I calculate that:
(rA)2 = (sqrt[(a)2 + (a)2])2 = 2a2
(rB)2 = (sqrt[(-a)2 + (a)2])2 = 2a2
(rC)2 = (a)2 = a2

So that:
I = m(a2 + 2a2 + 2a2) = 5ma2

But the answer is supposed to be 4.12ma2. What am I doing wrong?
 
Physics news on Phys.org
atlantic said:
So that:
I = m(a2 + 2a2 + 2a2) = 5ma2
Looks good to me.

But the answer is supposed to be 4.12ma2. What am I doing wrong?
I don't think you're doing anything wrong. What book are you using?
 

Similar threads

Correct Use of the Parallel Axis Theorem for Moment of Inertia
  • · Replies 2 ·
Replies
2
Views
2K
Moment of inertia of a disk about an axis not passing through its CoM
  • · Replies 11 ·
Replies
11
Views
4K
Parallel Axis Theorem Not Working
  • · Replies 28 ·
Replies
28
Views
2K
Moment of inertia of a rectangular prism parallel to one face
  • · Replies 11 ·
Replies
11
Views
1K
Solving for 'a' with Torque, Force, and Mass Moment of Inertia
  • · Replies 3 ·
Replies
3
Views
2K
Moment of inertia of T bar about 3 axes
  • · Replies 21 ·
Replies
21
Views
3K
Moment of inertia of a disc using rods as differential elements
  • · Replies 8 ·
Replies
8
Views
2K
Moment of inertia of a rod bent into a square
  • · Replies 12 ·
Replies
12
Views
2K
Moment of inertia of a cuboid parallel to one of its faces (repost with diagram)
  • · Replies 25 ·
Replies
25
Views
2K
What is the "r" in the moment of inertia?
  • · Replies 13 ·
Replies
13
Views
3K