How to Calculate the Moment of Inertia for a Rod and Sphere System?

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Homework Help Overview

The discussion revolves around calculating the moment of inertia for a system consisting of a rod and a sphere. Participants are provided with the length and mass of the rod, as well as the radius and mass of the sphere, along with the location of the axis of rotation.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss attempts to calculate the moment of inertia of the rod using integration, while expressing difficulty in determining the inertia of the sphere around the specified axis. There are inquiries about the clarity of the problem statement and requests for better visual aids.

Discussion Status

Some participants have suggested that integration may not be necessary and have mentioned the use of standard formulas and the parallel axis theorem as potential approaches. There is acknowledgment of the parallel axis theorem, with participants expressing gratitude for the guidance provided.

Contextual Notes

There are indications of missing information regarding the problem setup, and some participants note a lack of instruction on relevant concepts in their prior education.

Mohamed Essam
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1. The problem statement, all variables and given/known
See attachment , it only gives me length of rod and it's mass and radius of sphere and its mass and the place of the axis

Homework Equations


I=mr^2

The Attempt at a Solution


I tried to get the moment of intertia of rod by integration from -L/4 to 3L/4 , but i cannot get the intertia of sphere around the axis ,
 

Attachments

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Mohamed Essam said:
1. The problem statement, all variables and given/known
See attachment , it only gives me length of rod and it's mass and radius of sphere and its mass and the place of the axis

Homework Equations


I=mr^2

The Attempt at a Solution


I tried to get the moment of intertia of rod by integration from -L/4 to 3L/4 , but i cannot get the intertia of sphere around the axis ,
Can you post a better image please? That one is way too dark to read...
 
IMG_0498.JPG
berkeman said:
Can you post a better image please? That one is way too dark to read...
 
Mohamed Essam said:
I tried to get the moment of intertia of rod by integration from -L/4 to 3L/4 , but i cannot get the intertia of sphere around the axis
You should not need to do any integration. For such a question, I would expect to be allowed to quote standard formulas for moments about mass centres and apply the parallel axis theorem.
 
haruspex said:
You should not need to do any integration. For such a question, I would expect to be allowed to quote standard formulas for moments about mass centres and apply the parallel axis theorem.
by this equation ( Inertia at axis =Inertia at axis from centre of mass + mass*distance between the two axis^2 ) ??
 
Mohamed Essam said:
by this equation ( Inertia at axis =Inertia at axis from centre of mass + mass*distance between the two axis^2 ) ??
Yes.
 
haruspex said:
Yes.
Thank you for telling me the way of parallel axis theorem i wasn't know it , my physics professor in university didn't tell us anything about it and he puts it in an exam
 
Mohamed Essam said:
Thank you for telling me the way of parallel axis theorem i wasn't know it , my physics professor in university didn't tell us anything about it and he puts it in an exam
That's quite an omission. All good now?
 
haruspex said:
That's quite an omission. All good now?
Yeah , thank you so much.
 

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