Moment of inertia help, please

Click For Summary
SUMMARY

The discussion centers on calculating the moment of inertia for a system consisting of a rod and a sphere. The rod has a length L and mass M, with a point mass m located 3/4 L from one edge. The sphere, with mass m1 and radius R, is positioned at the opposite edge. The correct formula for the moment of inertia is I = (1/3)ML^2 + m(0.75L)^2 + (2/5)m1R^2, utilizing the parallel axis theorem for the sphere, not the point mass.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with the parallel axis theorem
  • Knowledge of rotational dynamics
  • Basic physics of rigid body motion
NEXT STEPS
  • Study the derivation of the moment of inertia for different shapes
  • Learn about the parallel axis theorem in detail
  • Explore applications of moment of inertia in engineering problems
  • Investigate the effects of mass distribution on rotational motion
USEFUL FOR

Students and professionals in physics, mechanical engineering, and anyone involved in dynamics and rotational motion analysis.

*best&sweetest*
Messages
36
Reaction score
0
This should be simple but I'm not sure whether I'm doing it right or not...
I have a rod rotating about its edge #1. Rod's length is L and its mass is M. There is a point mass m on the rod, 3/4 L away from the edge #1, and on the other edge (#2) there is a sphere of radius R and mass m1. I need to find the moment of inertia of the whole system. I know that I need to use parallel axis theorem for the point mass, but what should I do with the sphere?
Is it I = (1/3) ML^2 + m (0.75L)^2 + m1*(L)^2 + (2/5)m1*R^2
or I = (1/3)ML^2 + m (0.75L)^2 + (2/5)m1*R^2?
I think it is the first option, but I'm not sure.
Thank you!
 
Physics news on Phys.org
*best&sweetest* said:
This should be simple but I'm not sure whether I'm doing it right or not...
I have a rod rotating about its edge #1. Rod's length is L and its mass is M. There is a point mass m on the rod, 3/4 L away from the edge #1, and on the other edge (#2) there is a sphere of radius R and mass m1. I need to find the moment of inertia of the whole system. I know that I need to use parallel axis theorem for the point mass, but what should I do with the sphere?
Is it I = (1/3) ML^2 + m (0.75L)^2 + m1*(L)^2 + (2/5)m1*R^2
or I = (1/3)ML^2 + m (0.75L)^2 + (2/5)m1*R^2?
I think it is the first option, but I'm not sure.
Thank you!
Option 1 loooks correct, but actually, you used the parallel axis theorem for the sphere, not the point mass, which is correct.
 

Similar threads

Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 13 ·
Replies
13
Views
3K
Replies
8
Views
2K
  • · Replies 28 ·
Replies
28
Views
2K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 21 ·
Replies
21
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K